I'd say start by studying a money market diagram, which basically informs the LM curve. If you understand that, then you will start to understand the LM curve much more. IS/LM is really tricky, but it's also really useful in general discussions of monetary policy and such... it's worthwhile to learn, but definitely takes time to fully grasp.

Also, when they say "interest rate", they basically mean general market interest rates. It's a catchall, really, for bonds.

The Fed screws around with money supply through open market operations - buying or selling bonds to the public - and this affects a variety of different interest rates, which are all put under the umbrella of "interest rate". This stuff gets a little confusing, and there's a lot of things in the banking system to study in order to understand exactly why the Fed can do this.