While discipline and patience are closely related, they are different in a sense as well. Discipline of course is the ability to stay the course of action, while patience is more the understanding of why it's best to do so. If you have the proper amount of patience, it thus becomes easier to have the proper amount of discipline.
So the key to patience really is thinking more about what your goals are rather than getting caught up too much in the moment to moment action. For example, you want to think more on how certain moves are going to affect your play in the long run rather than just worrying about right now.
Here's an example which comes up a lot. In order to play correctly this involves a whole lot of folding. You don't get the cards you want pre-flop so you throw them away. You didn't hit your hand later so you usually are going to want to throw it away as well, unless there's a good reason not to. Now, with things being what they are, sometimes you can go on streaks where that's pretty much all you're doing - throwing hands away. It's not very difficult to have your patience tried in these situations. Perhaps you crave more action than what you've been getting. Perhaps you grow weary of not having won a hand in a while and are looking to try to force things more. Whatever the reason, the lack of luck over the last while is causing you to want to relax your standards and play in a way that you have determined isn't in your best long term interests.
Now, it's true that by being disciplined enough you'll be able to resist these temptations. Hopefully you will in fact. However, keep in mind that what you are resisting is giving in to your lack of patience, and the more impatient you allow yourself to become, the more difficult it will be to resist. A better approach, one that will lead to more success, is to reflect the root cause of the matter, which boils down to not allowing yourself to lose touch with the rationale that has you playing this way in the first place.
Let's say for instance you get dealt KTo in early position. Now this is a playable hand in a lot of cases in late position, but isn't something you want to normally consider playing here. To add to things, there's a fair bit of raising at the table and if you play this chances are someone will put in a raise, and now you'll be put on a decision to call an additional bet with a hand you could be in trouble with even if you hit it. That's the very reason why you fold this hand in this position in fact.
However, this is the best hand you've seen in awhile and you think that it might be awhile before you see another decent one like this, the way you see the cards going. So you think - what's the harm, it's only a small bet, and maybe no one will raise and you'll have the best hand probably going into the flop. And you haven't won a hand in a while so you're due. And you're growing tired of just folding. So what the heck, you do it.
Someone does raise though, and you end up tossing it anyway. Or, due to your increasing frustration, you may call the raise, in spite of the fact this person doesn't raise often and very likely has a better hand than you. The mistake you've really made here, in addition to not having the discipline to stick to your guns, is to have let your normal understanding of poker strategy get clouded over by the frustration of the moment.
Instead, when you have such an urge, what you need to be doing here is approaching the situation from a more long term view. Therefore, instead of telling yourself you might get lucky with this hand, look toward what would happen if you acted this way as a general rule. Of course, what would happen is that you'd throw the hand away a lot, and get caught as well a lot when you don't. This is why in most situations good poker players will agree it's a fold here. You understand why, and need to do the same, because if you don't, the move will end up costing you money in the long run.
This is just an example of course, but as you can see the problem here arises from not properly reflecting on the overall long term outcomes of actions you're considering taking at the table. With proper reflection, not just things like talking yourself into the fact that a player may be bluffing even though there's no real good evidence of this, and the like, you'll find that playing with the proper amount of patience will come much easier, and in turn, the discipline needed to stick with your thought out plans of action will come easier to you as well.