user5640: In the days before LCDs and digital cameras, manually focusing an interchangeable lens still camera wasn't a whole lot different than it is today. In most designs, you had a mirror that gave the photographer a through-the-lens view, allowing them to accurately focus. When the shutter button was pressed, the mirror flipped out of the way, exposing the film.
However, this method is obviously not usable for the continuous focusing required by video camera operators. Modern cameras solve this problem by using Live View. How was this problem solved in the film days?

user2598: There are two main ways this was solved:
1. Measuring Focus
When using this method, the focus puller measures the distances at every point during the shot, and then pulls focus to these marks, at times making adjustments when an actor or grip misses their mark.
This still occurs today, however is becoming less prevalent due to the filmmaking styles being used (handheld, where the same marks are not hit each time).
2. Video Assist
Using one of several methods, including half-silvered mirrors, CCD sensors behind the film negative, and telecine transfers, a video split is made. On modern productions shooting on film, this split is what is sent to 'Video Village', where the director sits.
Telecine Transfer (Not the correct term)
I've never really understood how it worked, until now, so I present this lovely diagram from Wikipedia:

In essence, the light shines in and exposes the negative. After that, it passes through a series of half-silvered mirrors, each time being split into separate light components and recorded onto an imaging chip. These are them combined, and displayed in the viewfinder, or as a video-out.
One side effect of this method, is the mechanical shutter is visible, as a black screen lasting 1/50th of a second, 25 times a second (whenever the negative itself is not exposed).
3. Parallel Sight
Common throughout the 1950s and 60s, having a parallel sight (separate lens, like what you had on a cheap film point-and-shoot camera) allowed the operator to see approximately what was being exposed onto the negative.
4. Half-Silvered Mirror
Update: Added from AJ Henderson's comment below.
As mentioned in the comment, a very cheap way of getting an image to a viewfinder was to simply use a half-silvered mirror, somewhere between the lens and the negative. In this way, half the light transmitted through the lens exposes the negative, and half is seen through the operator's viewfinder.
This method does not allow for multiple viewfinders, monitors, or screens, unless another split is created.

user1950: Good quality film cameras have a reflex viewfinder system, where "reflex" means that you're viewing through the lens, and thus you can judge focus by eye. 
To achieve this There are, er were, two basic strategies: 

Split the beam of light from the lens with a prism or half silvered
    mirror, meaning that most of the light goes to the film, and a bit
    goes to the viewfinder.    Advantages: no shutter flicker,
    cheaper. Disadvantages: less light,    both for exposing the
    film, and a dimmer image in the viewfinder (in    low light
    situations it can make it difficult to focus or even see what's
    going on).    This is how my Bolex camera does it.

Position a revolving mirror between the lens and the film plane. While the film is being pulled down by the sprockets the mirror
moves into place, bouncing the light into the viewfinder, and once
the film is ready to be exposed, the mirrors swings around and the
viewfinder goes temporarily black. It's basically what an SLR camera
does, but instead of flipping up the mirror is rotating.
Advantages: more light for the film and the viewfinder, one less optical element in the light path, ability to vary the angle of the
shutter allowing for fine control over exposure without affecting
the depth of field. Disadvantages: More complicated
(=expensive), flicker in viewfinder (actually I think this is
something of an advantage, because you always could tell when the
camera was running, and also when filming video displays you could
make sure that the balck bar was visible in the viewfinder, and
therefore not visible to the film), some degree of rolling shutter.This is how my CP16 does it, as well as pretty much all professional
cinema cameras.
 the mirror is the thing that looks like a bow tie.

As you can see, both methods allowed the operator to see through the lens while filming, allowing for on-the-fly focusing. Video splits also allowed a live video feed to be set up, meaning the focus puller (and director etc.) could have a monitor, but this was relatively late in the piece. A video split is basically a video camera bolted on to where the eyepiece goes, or sometimes with a separate beam-splitter. Until video splits came along the focus puller checked the focus points in the rehearsal, made marks on the floor with camera tape, consulted their cinematographer's manual for the depth-of-field charts, and eyeballed it.
You'n whippersnappers don't know how easy you gots it. Now get off my lawn!

5640: <p>In the days before LCDs and digital cameras, manually focusing an interchangeable lens still camera wasn't a whole lot different than it is today. In most designs, you had a mirror that gave the photographer a through-the-lens view, allowing them to accurately focus. When the shutter button was pressed, the mirror flipped out of the way, exposing the film.</p>

<p>However, this method is obviously not usable for the continuous focusing required by video camera operators. Modern cameras solve this problem by using Live View. How was this problem solved in the film days?</p>
 2598: <p>There are two main ways this was solved:</p>

<h1>1. Measuring Focus</h1>

<p>When using this method, the focus puller measures the distances at every point during the shot, and then pulls focus to these marks, at times making adjustments when an actor or grip misses their mark.</p>

<p>This still occurs today, however is becoming less prevalent due to the filmmaking styles being used (handheld, where the same marks are not hit each time).</p>

<h1>2. Video Assist</h1>

<p>Using one of several methods, including half-silvered mirrors, CCD sensors behind the film negative, and telecine transfers, a video split is made. On modern productions shooting on film, this split is what is sent to 'Video Village', where the director sits.</p>

<h2><strike>Telecine Transfer</strike> (Not the correct term)</h2>

<p>I've never really understood how it worked, until now, so I present this lovely diagram from Wikipedia:</p>

<p><img src="https://i.stack.imgur.com/FqiaC.png" alt="enter image description here"></p>

<p>In essence, the light shines in and exposes the negative. After that, it passes through a series of half-silvered mirrors, each time being split into separate light components and recorded onto an imaging chip. These are them combined, and displayed in the viewfinder, or as a video-out.</p>

<p>One side effect of this method, is the mechanical shutter is visible, as a black screen lasting 1/50th of a second, 25 times a second (whenever the negative itself is not exposed).</p>

<h1>3. Parallel Sight</h1>

<p>Common throughout the 1950s and 60s, having a parallel sight (separate lens, like what you had on a cheap film point-and-shoot camera) allowed the operator to see approximately what was being exposed onto the negative.</p>

<h1>4. Half-Silvered Mirror</h1>

<p><strong>Update: Added from AJ Henderson's comment below.</strong></p>

<p>As mentioned in the comment, a very cheap way of getting an image to a viewfinder was to simply use a half-silvered mirror, somewhere between the lens and the negative. In this way, half the light transmitted through the lens exposes the negative, and half is seen through the operator's viewfinder.</p>

<p>This method does not allow for multiple viewfinders, monitors, or screens, unless another split is created.</p>
 1950: <p>Good quality film cameras have a reflex viewfinder system, where "reflex" means that you're viewing through the lens, and thus you can judge focus by eye. </p>

<p>To achieve this There are, er were, two basic strategies: </p>

<ol>
<li><p>Split the beam of light from the lens with a prism or half silvered
    mirror, meaning that most of the light goes to the film, and a bit
    goes to the viewfinder.    <strong>Advantages</strong>: no shutter flicker,
    cheaper. <strong>Disadvantages</strong>: less light,    both for exposing the
    film, and a dimmer image in the viewfinder (in    low light
    situations it can make it difficult to focus or even see what's
    going on).    This is how my Bolex camera does it.</p>

<p><img src="https://i.stack.imgur.com/oJywi.jpg" alt="promotional picture showing light path in a bolex camera"></p></li>
<li><p>Position a revolving mirror between the lens and the film plane. While the film is being pulled down by the sprockets the mirror
moves into place, bouncing the light into the viewfinder, and once
the film is ready to be exposed, the mirrors swings around and the
viewfinder goes temporarily black. It's basically what an SLR camera
does, but instead of flipping up the mirror is rotating.
<strong>Advantages</strong>: more light for the film and the viewfinder, one less optical element in the light path, ability to vary the angle of the
shutter allowing for fine control over exposure without affecting
the depth of field. <strong>Disadvantages</strong>: More complicated
(=expensive), flicker in viewfinder (actually I think this is
something of an advantage, because you always could tell when the
camera was running, and also when filming video displays you could
make sure that the balck bar was visible in the viewfinder, and
therefore not visible to the film), some degree of rolling shutter.This is how my CP16 does it, as well as pretty much all professional
cinema cameras.</p>

<p><img src="https://i.stack.imgur.com/2zcCc.jpg" alt="rotating mirror in CP-16 camera"> the mirror is the thing that looks like a bow tie.</p></li>
</ol>

<p>As you can see, both methods allowed the operator to see through the lens while filming, allowing for on-the-fly focusing. Video splits also allowed a live video feed to be set up, meaning the focus puller (and director etc.) could have a monitor, but this was relatively late in the piece. A video split is basically a video camera bolted on to where the eyepiece goes, or sometimes with a separate beam-splitter. Until video splits came along the focus puller checked the focus points in the rehearsal, made marks on the floor with camera tape, consulted their cinematographer's manual for the depth-of-field charts, and eyeballed it.</p>

<p>You'n whippersnappers don't know how easy you gots it. Now get off my lawn!</p>
