You should probably read some books on this stuff, as there are lots of them around. The classic text is "Design Patterns" by Gamma, Helm, Johnson and Vlissides (the "gang of four"), which has lots of patterns including many you may never need. For a quick start that will focus on the more commonly used patterns, try the excellent "Head First Design Patterns" by Freeman and Freeman. Craig Larman's book "Applying UML and Patterns" is good too, although it covers UML and OO design in general, not just patterns.
However, be careful about how you use patterns. I've worked on a few projects where people have basically used every pattern they could find in all the Java
JEE sample applications, regardless of whether the project actually needed them.