Also, if I am a goalie, and the other team is not shooting on me, how can I show my game?
Coaches know goalkeepers touch the ball with their hands a very limited number of times during a match. It is very important for goalkeepers to have highlight videos (but full-game is often appreciated too), training videos, etc., as one game is (usually) never enough to determine a GK's quality.
During my DD's recruiting process, coaches would come to watch sessions with her goalkeeper coach to see her work ethic, technique, etc. During this time, she was also on an ECNL team that faced what seemed like an infinite amount of shots most games, so she was able to showcase her abilities. However, the main things coaches always looked for, despite the circumstances, were:
1. A good, technical, high energy warm-up.
2. Good, firm communication with the team, although no talking just for the sake of hearing their own voice.
3. Ability to act as another field player (playing out of the back, being an option for your defenders, all depending on their team's style of play).
4. Distribution with a purpose/target, not just punting to punt.
5. A sense of confidence and joy in the game, or body language. Even if your player isn't always involved, does it look like they want to be there?
6. And finally, doing the simple things consistently well! Goalkeepers face a lot of "basic" shots and being able to consistently deal with them gives the coach a sense of reliability in the player. Positioning is key, as well as the ability to deal with crosses, have proper technique in a pass, knowing when to stay or go in a 50/50-like situation, etc.
Like many have said, different coaches look for different things and everyone has different experiences in the recruiting process. However, I bet most coaches can agree they look for at least one of the things stated above!
Hope this helped.