In Red Dead Redemption for Xbox 360 and PS3, you can’t necessarily save your game at any time, which can be a pain in any game where you can die at any point.
To save your game anywhere, all you need to do is purchase two different horse deeds. When you use those deeds to summon a horse, your game will save automatically. Since you can’t re-summon a horse you already have out, that’s why you need two deeds, so you can switch horses if you have one summoned already.
Another method to save your game quickly (though at limited locations unfortunately) is to play a quick game of Five Finger Fillet. Win a cheap game and quit, and your game should do an auto-save. I know this doesn’t allow you to save anywhere, but it can help if you need to save your game and don’t have access to two horse deeds yet.