First, it's best that you start by checking your amp to make sure the volume is turned down. Bad things can happen if your amp is turned up when you kick it on. By bad, I mean loud, destructive noise which can in some cases damage your speakers. If you are plugging in an electric guitar, you could also make sure it is turned down as well, just to be safe.
Next, inspect the cable you are going to use. If the ends of the cable have screw-on type connectors, make sure they are tight on both ends before you plug in. You should also check that there are no bent or broken connectors, frayed sections, or exposed wiring along the cable that will cause feedback or other electrical disasters.
After you have checked the cable, plug it into the guitar or the amp, ensuring a complete connection. You will often hear an audible "click" letting you know the connection is solid. Then plug the other end of the cable into the amp or guitar, whichever remains.
Now, go ahead and turn on the amp, and bring up the volume some. If you have levels 1-10 on the dial, try 2 or 3. If your guitar has a volume knob, now is the time to turn it up. Strum a few chords or play some licks and adjust as needed.
Following these steps can save you a lot of grief and possibly a lot of money.