It's very difficult. However, there are various routes available to you.
Perhaps the most obvious would be to either join or start a Jedi-like religion. Here's one: http://templeofthejediforce.org/
That is not necessarily the most satisfying way to become a Jedi, though. Doing something like that lacks a lot of the characteristics of being a Jedi. For one, you will most likely not earn the admiration and respect of those around you like a Jedi would. It is doubtful that you would be seen as someone to go to when people need help or answers, unless you are already seen that way.
One group of people that are frequently compared to being like the Jedi are the Shaolin monks. Indeed they seem to share many similarities to the Jedi. So you can always hop a plane to China and try to join their monastery.
If you are not that willing to so radically alter your life, you may wish to pursue a more local option. Several professions share many similarities to the Jedi order. Two immediately come to my mind:
1. The military. If you choose this option I would recommend trying to join as/become an officer, as their roles seem more in tune with being a Jedi. There are still many differences, of course.
2. The academy. Now this is one I do not think most people would normally think of, but the academic life does share a great deal in common with the life of a Jedi. You are trained in it from a very young age, but keep being an apprentice well into adulthood. If you do not start at a young age you pretty much cannot enter later (i.e. if you didn't go to elementary school as a child you will have a hard time getting into graduate school). Many people who start on the journey do not finish it (although this is not really the same as you don't go to elementary school with the intention of becoming a professor). You get a special title that everyone calls you by (i.e. "Doctor") regardless of what exact specialty you are in. People generally respect you and look at you as someone who knows something. You spend part of your time solving the world's problems (i.e. research) and part of your time training your apprentice(s) (i.e. teaching). There is no uniform but everyone tends to dress similarly. There is a non-extensive ranking system (i.e. associate, assistant, and full professors; Jedi and Jedi Masters), and higher ups cannot always just order the lower ones around. You can even say that it is a life of sacrifice as one could probably make more money working for a corporation. You can keep going in this line of thought to find more similarities, but of course you will also find many differences. One big one is that this profession will generally not teach you any special combat techniques or give you any physical power. You will get a fair bit of non-physical power (e.g. control over the fates of students) as well as a boat-load of perceived power, though.
I am sure you can think of other professions that may be similar to being a Jedi and may satisfy this desire I assume that you have. Remember, though, that in the end a Jedi would always be a Jedi no matter what their situation. So even if your life seems to be the opposite of what being a Jedi is like, think what a Jedi would do in your situation: they would still behave like a Jedi. In this sense, the religious-type groups I mentioned above are on to something.
(EDIT)
It is also possible to become a real Jedi by joining one of the many online training sites. These include the Real Jedi Knights (RJK), and The Jedi Order (TJO) and many others. These websites are dedicated to training people who show interest in becoming REAL Jedi, and not just RPGers. (Edit by Jedi High Knight Anthony)