First off, you need to be sure you have JDK 7 (Java Development Kit version 1.7) installed on your computer. If you are using the Snow Leopard release of Mac OS X, then you are fine; if you have an earlier version of Mac OS X, see one of us. If you have a Windows computer, then unless you have installed JDK 7, you should do so now (explained in the next step). If you are using Linux or some other operating system, see one of us.
If you need to install JDK 7 and are on a non-Mac platform, then go to Oracle's download site and click the Download JDK button (in the Java Platform, Standard Edition box) and follow their instructions. The process is fairly straightforward; if you have any problems/questions see one of us.
After making the choice above, go ahead and download and install the files. You are probably best off using the default choices they give you for where Eclipse is installed. Again, the process is fairly straightforward; if you have any problems/questions see one of us.
Once you have it installed, fire it up and see how/whether it works.
We will give more instruction on how to use SLIME during lectures.