The answer is: Maybe you can't.
And rather than stewing in frustration for months or even years, it's better to determine whether the thing that's driving you crazy is ever going to change. If not, your quality of life will be much higher if you stop focusing on how much it irritates you and, instead, choose to accept it, and decide how you want to respond.
The first step is to talk with your manager, and pay close attention to what you hear in his or her response, both spoken and unspoken.
For instance, say you have a boss who constantly reneges on commitments. She tells you she's going to meet with you at 2 p.m., and by 4 p.m. you haven't heard from her. She tells you she'll talk to that unreliable vendor for you, and it never happens. You're frustrated because you can't rely on her word, and maybe also a bit angry because you could never get away with that behavior. Stop stewing. Instead, sit down with her and explain the behavior's effect on you, and ask for what you want.
You may hear upfront that the behavior isn't going to change. She might tell you, for example, that the demands of her schedule make it unlikely she could do things differently. If that's the case, then it’s time to accept that this is the reality of working with her—for as long as you're working with her. Instead of being irritated, be grateful she's given you the truth about what to expect. (You can also ask her for some smaller, possibly easier, modifications, such as warning you in advance when she realizes she's going to renege on something.)
You may, instead, get a promise that she'll change. In that case, watch and wait. Does anything really change? If not, then the advice above applies to you too, because actions, not words, will give you the information you need here. I've seen many people have the same conversation over and over with their manager for years—promises are made, promises are broken, and the employee keeps trying, inexplicably expecting a different result next time.
What if all signs point to low probability of change? Then you figure out if you can find ways to live with the situation—as it is, not as you want it to be—and still be reasonably happy. If you can't, then accept that you can't, and start looking at other jobs. But often, once you stop agonizing over whatever it is that's irritating you and accept it as part of the package, you can find ways to live with it peacefully.
The upshot? Don't get so focused on your desire to change the person that you lose sight of whether that change is something you're ever likely to get. Commit to seeing and dealing with the reality of the situation, and make your decisions based on that reality.
Alison Green is the author of Managing to Change the World: The Nonprofit Leader's Guide to Getting Results. She is chief of staff for the Marijuana Policy Project, a nonprofit lobbying organization, where she oversees day-to-day management of the staff as well as hiring, firing, and staff development. Her writings have been published in the Washington Post, the New York Times, Maxim, and dozens of other newspapers. She blogs at Ask a Manager.