Mic fright
1.) You are just a person talking to another person or group. Dont think of yourself on stage or as a radio DJ, you are just talking. So talk. Talk like you are on the phone. Talk like you are talking to the guy next to you. Talk like you are in a huddle for a game of touch football. Just push the button and talk - you don't have to be "Joe Cool".
2.) Before you push the button! Reherse. Not at home, not at the school - in your head. RedHeadCFI gave some good general tips, but read the AIM - Section 4-2-1 thru 4-2-14 and know your roles (section 5-5). If you are on the 45 to downwind at your home airport and need to make the call - think about what you are going to say - what's important and what's not. What is important is the kind of airplane and your relative position. Ergo: "Podunk traffic, Cessna 18-Kilo is on a 3 mile forty-five to runway one-niner." Say it in your head, then push the button and say it in the Mic.
3.) The uncontrolled field stuff is pretty easy because you are going to do the same thing almost every time. Call for advisories, announce entering the (usually 45) pattern, downwind, base and final. (PS. "Clear the active" intentionally omitted due to its redundancy at most airports!). Leaving, you do a radio check, announce the departure and maybe leaving the pattern if other traffic is inbound or definitely announce your intentions to stay in the pattern. Know what the calls are before you try to make them.
4.) When you get to control towers and ATC in general, you have to learn the "dance". Again in general, it's who you are, where you are and where you want to go. Sounds simple but there's a lot of info that has to be delivered pretty quickly. After the initial call up, the dance has begun. ATC will tell you to do something and you comply - often times you just repeat or parrot the commands right back.
TWR: "Cessna 18-kilo, make left base runway 23, report 3 miles"
18K: "Cessna 18-kilo left base runway 23 (and will report)"
The parentheses is an option. In the old days we would add "wilco" for will comply but this fell out of favor because people just started answering "wilco" or just "roger" and ATC was left with a hollow feeling of whether the pilot got the whole instruction. I add the "will report" because ATC told me to do two things and I am answering that I know both things - make a base and make a call. I don't just parrot a "report" phrase because that is followed with the question, "18-kilo, are you at 3 miles now?"
Like I said, this is a dance and you have to work with your partner.
5.) When working with ATC, the first step in the dance is you knowing stuff first. You have to be prepared - get the ATIS or AWOS for the airport. Know the FBO on the field and have a map of the airport with taxiway names. It's tough right now with 9.5 hours, but we talk about a person being ahead or behind the airplane. A person who is behind has planned nothing. A person looking ahead, knew minutes ago that they had to listen to ATIS, they knew they had to provide the answers to where they are now and where they want to go, call ATC, get instructions for the airport or airspace and comply. Which sounds better?
34K: "Philly Approach, Cessna 34-kilo."
or
34K: "Philly Approach, Cessna 1234-Kilo, information Zulu."
6.) Get your instructor involved. The easiest lessons to teach are the one's where the student admits not understanding. Tell him or her that you are having a problem. The solution will be that you make more of the calls, but practice makes perfect.
Good luck. Aviate, Navigate, Communicate.
Radio shack makes a $9 (might be $12 now) cheap transitor radio that picks up aviation VHF frequencies. You can just drive out to the airport and listen to other folks making calls. Rate the calls - give somebody a "9" for clear, simple, calls that you like. Give 'em a "2" for ums and ahs or rambling calls that take a lot of air time.