A shofar can be made from the horn of any animal other than a bull, the most common animals are the Ram and the Kudu Antelope.
The difference between a ram's horn and an antelope's horn lies in the size and shape. A ram's horn is short, about a foot long and contains a single bend. Kudu horns can be almost four feet long and spiral. I personally prefer the deeper sound of a kudu, but also have found ram's horns to be easier to use.
Fun Fact: It's a mitzvah to hear the shofar blown, but not to blow it.
(A mitzvah is a commandment - so to follow a commandment is to perform a mitzvah. There are 613 mitzvahs in the Torah.)
Step 1: Make Some Noise
You'll want a tight upper lip, and looser lower lip, then when you blow out, your lips will vibrate. Put the mouthpiece against your lips (not inside your mouth) and try to force air through as small a hole in your lips as possible. I put the shofar in the corner of my mouth, others use the center..it's up to you. I also use my fingers and wear ChapStick to help create a good seal.
The goal isn't to force as much air out as possible, so don't tire yourself trying to make a sound. It just takes practice.