If you find that your current alliance is not the place for you, you are allowed to switch at various point levels, which are described below.
The most important is that you will lose any specialty ships you own that belong to the alliance you're leaving, regardless of how you obtained them. You will also be required to fill out a new specialty starship application for the alliance you're now joining.
The point levels are 1500, 2500, 5000, 10000, 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000, and 55000. This means that if you have under 1500 points, you cannot switch. Once you hit 1500 points, however, you are able to switch your alliance. You won't be able to switch again until you get 2500 points. The confusing part happens when you have, say, 5000 points. If you switch your alliance at 2500 points, you cannot switch again until you hit 5000 points. You do not get "credit" for any point levels you passed without switching your alliance.
There is a 300 million credit fee associated with switching alliances.
Visit the Interalliance Relation Center on Pax and type MENU. It should be self-explanatory from there.