user201: When I meditate, I usually sit in what is referred to in the United States as Indian style.  The problem with this position is twofold: 1) It isn't very stable and 2) after ~15 minutes I find myself straining to keep upright.  I have been told that the full lotus position is more stable since the legs are symmetric and both knees are on the ground.  I've tried to get myself into the position, but I am not even flexible enough to get into the half lotus position (one foot on the other knee).  
My question is: If I am willing to work at it daily; what is the best way to get my legs flexible enough to sit in the full lotus position?  

*Picture from "Tanumânasî en Meditacion Loto Padmasana" by Jesús Bonilla (Tanumânasî) - Retiros de yoga. Licensed under Public domain via Wikimedia Commons.

user883: here I can answer as a sporter ;)
Your problem is twofold: 

Your range of motion is limited,  and
your core is not strong enough

To address 1. you can do stretching, common gymnastics stretching: Guide to basic stretching. Yoga is also a good option but I consider common stretching more to the point (and you will need that for yoga too, anyway). 
For 2. there is no easy answer: You need to strengthen  your core. Please note that for many Japanese, Koreans and Indians the lotus position is easy because they use to sit on the ground, this has a huge impact on  the core muscles: Our western chairs hold our backs and void us from using too much force for sitting, making that our cores are less strong, specially a large amount of small muscles... 
There are two basic exercises that you can do for that: the plank and the bridge: 10 core workouts
For both, the core exercises and the stretches you can start holding them for 20 seconds, build up to 30 seconds and then up to 1 min and 1:30, there is a maximum of 90 seconds (1:30) above which there is no effect. I fact the proper stretching reflex of the muscles is triggered after 20-30 seconds after which they elongate.
Other things that you may do are: 

Stand as much as you can: If you drive by train don't sit. If you are in public spaces try avoid sitting and stand instead. 
Use the stairs not the escalators/mechanic stairs.
Give sitting on the ground a try, even when not for meditation

So, here's my grain of salt. I'm not a Buddhist, mind you, I practised Zen a lot of years ago, but I recall zazen being very painful to hold while now I can sit comfortably in the lotus position or seiza (the real one, as in Kendo).

user832: Yoga is very helpful, especially aspects that deal with opening the hips and stretching the legs. It is best not to force it or you could hurt the body.
A cushion or zafu under the tail bone and buttocks can elevate the body sufficiently so crosslegged is more comfortable.
Some people sit Japanese style with legs folded under sitting on your heels and or supported by a zafu.
Sitting in a chair with a straight back and feet on the ground is a valid method of meditating. The position will open up and be comfortable over years as the practice opens up the locked up sections of the body.
Here is a youtube video that especially works on opening for beginners. Adrienne has many yoga videos. She seems like a meditator as she encourages mindfulness expecially in 2nd video. She is conservatively dressed and friendly in her approach. I find her a helpful teacher that does not provide unneeded distractions.
20 minutes complete beginners - very doable sequence.
https://www.youtube.com/watch?v=v7AYKMP6rOE
40 minute longer more meditative from the preview.
https://www.youtube.com/watch?v=OQ6NfFIr2jw&list=PLqkIhuaKSFbuaG3i9cBpO7E0dAKnd-MAu
Accepting where you are is important. You are right where you need to be. You are opening in a very natural way. Namaste.

201: <p>When I meditate, I usually sit in what is referred to in the United States as Indian style.  The problem with this position is twofold: 1) It isn't very stable and 2) after ~15 minutes I find myself straining to keep upright.  I have been told that the full lotus position is more stable since the legs are symmetric and both knees are on the ground.  I've tried to get myself into the position, but I am not even flexible enough to get into the half lotus position (one foot on the other knee).  </p>

<p>My question is: If I am willing to work at it daily; what is the best way to get my legs flexible enough to sit in the full lotus position?  </p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/7/7d/Tanum%C3%A2nas%C3%AE_en_Meditacion_Loto_Padmasana.JPG" alt="Picuture from Wikimedia Commons">
*Picture from "<a href="http://commons.wikimedia.org/wiki/File:Tanum%C3%A2nas%C3%AE_en_Meditacion_Loto_Padmasana.JPG#mediaviewer/File:Tanum%C3%A2nas%C3%AE_en_Meditacion_Loto_Padmasana.JPG" rel="nofollow noreferrer">Tanumânasî en Meditacion Loto Padmasana</a>" by Jesús Bonilla (Tanumânasî) - Retiros de yoga. Licensed under Public domain via <a href="//commons.wikimedia.org/wiki/" rel="nofollow noreferrer">Wikimedia Commons</a>.</p>
 883: <p>here I can answer as a sporter ;)</p>

<p>Your problem is twofold: </p>

<ol>
<li>Your range of motion is limited,  and</li>
<li>your core is not strong enough</li>
</ol>

<p>To address 1. you can do stretching, common gymnastics stretching: <a href="http://www.mayoclinic.org/healthy-living/fitness/multimedia/stretching/sls-20076840?s=2" rel="nofollow">Guide to basic stretching</a>. Yoga is also a good option but I consider common stretching more to the point (and you will need that for yoga too, anyway). </p>

<p>For 2. there is no easy answer: You need to strengthen  your core. Please note that for many Japanese, Koreans and Indians the lotus position is easy because they use to sit on the ground, this has a huge impact on  the core muscles: Our western chairs hold our backs and void us from using too much force for sitting, making that our cores are less strong, specially a large amount of small muscles... </p>

<p>There are two basic exercises that you can do for that: the plank and the bridge: <a href="http://exercise.about.com/od/abs/ss/abexercises_10.htm" rel="nofollow">10 core workouts</a></p>

<p>For both, the core exercises and the stretches you can start holding them for 20 seconds, build up to 30 seconds and then up to 1 min and 1:30, there is a maximum of 90 seconds (1:30) above which there is no effect. I fact the proper stretching reflex of the muscles is triggered after 20-30 seconds after which they elongate.</p>

<p>Other things that you may do are: </p>

<ul>
<li>Stand as much as you can: If you drive by train don't sit. If you are in public spaces try avoid sitting and stand instead. </li>
<li>Use the stairs not the escalators/mechanic stairs.</li>
<li>Give sitting on the ground a try, even when not for meditation</li>
</ul>

<p>So, here's my grain of salt. I'm not a Buddhist, mind you, I practised Zen a lot of years ago, but I recall zazen being very painful to hold while now I can sit comfortably in the lotus position or seiza (the real one, as in Kendo).</p>
 832: <p>Yoga is very helpful, especially aspects that deal with opening the hips and stretching the legs. It is best not to force it or you could hurt the body.
A cushion or zafu under the tail bone and buttocks can elevate the body sufficiently so crosslegged is more comfortable.
Some people sit Japanese style with legs folded under sitting on your heels and or supported by a zafu.
Sitting in a chair with a straight back and feet on the ground is a valid method of meditating. The position will open up and be comfortable over years as the practice opens up the locked up sections of the body.</p>

<p>Here is a youtube video that especially works on opening for beginners. Adrienne has many yoga videos. She seems like a meditator as she encourages mindfulness expecially in 2nd video. She is conservatively dressed and friendly in her approach. I find her a helpful teacher that does not provide unneeded distractions.</p>

<p>20 minutes complete beginners - very doable sequence.
<a href="https://www.youtube.com/watch?v=v7AYKMP6rOE" rel="nofollow">https://www.youtube.com/watch?v=v7AYKMP6rOE</a></p>

<p>40 minute longer more meditative from the preview.
<a href="https://www.youtube.com/watch?v=OQ6NfFIr2jw&amp;list=PLqkIhuaKSFbuaG3i9cBpO7E0dAKnd-MAu" rel="nofollow">https://www.youtube.com/watch?v=OQ6NfFIr2jw&amp;list=PLqkIhuaKSFbuaG3i9cBpO7E0dAKnd-MAu</a></p>

<p>Accepting where you are is important. You are right where you need to be. You are opening in a very natural way. Namaste.</p>
