This applies to desktop as well (you'll find it in the bottom-right corner of the page). You should see a couple of options appear:   Photo (mobile)/Upload a pin (desktop) - Allows you to select a photo from your device's default "Pictures" album.  Website (mobile)/Save from a website (desktop) - Lets you search for a website (or enter a link to one), then search the resulting site for pin-compatible items. On mobile, you also have the option of tapping Copied Link to navigate to the last link you copied. This option is functionally the same as tapping Website. From here, uploading a pin will vary based on your choice:  If you chose to upload a photo, you'll have to allow Pinterest access to your device (mobile) or click Choose photos (desktop). You can then browse through your device's pictures to select the one you wish to upload. If you chose to use a website, you'll enter the website's URL into the provided text field. Once the site finishes loading, you should see a list of all media that you can pin--though, on iPhone, you must first tap Save in the top-right corner before you see this list. Again, this process will vary slightly depending on your chosen upload path, but you'll tap or click the photo you wish to save. Doing so will add your pin to the board in question. You can also add a description to your item in the field to the right of the item's icon.
Select the + icon again. Select your preferred option. Select an item to pin. Select a board when prompted.