Know your role. Ask the coach what your role is going to be. Closer? Long-relief? Set-up guy? The more you can narrow down your role the better you can predict when you will pitch and how to prepare.
Being a reliever can be both physically and mentally
challenging and needs to be handled well.
Know yourself. The toughest part about the pen is not knowing when you are going to pitch. A starter can plan and prepare days in advance. You can't. Every pitcher has different needs in terms of how much preparation is needed before pitching. Some guys can get ready in a flash. Some take longer. Know what your needs are and do whatever it takes to be ready when called on. If you take longer to warm-up, be the guy that warms up the outfielder prior to the inning. This keeps your arm somewhat loose throughout the game so that you don't need as much time to warm-up if called on. Monitor your arm and adjust your throwing routine as needed.
Don't rely on coaches. Managers have a million things to think about during the game and may be late in telling a relief pitcher to warm up. It's your job to make sure you are ready to go.
Pay attention. It's very easy to get distracted in the bullpen. Pay close attention to the game so that you can better predict when you might be needed. If you are a long-relief guy and you notice the starting pitcher is all over the place in the pen prior to the game, start your preparation - at least mentally. If you're a lefty and you know that a string of lefties is coming up later in the line-up, start moving around. Paying attention allows you to get going even before the coach tells you to. You should NEVER be caught off guard when they tell you to get up and start throwing. It's your job to get yourself ready. It's not the coaches' job.
MOVE! A pet-peeve of mine is telling a kid to warm up and watch him take his sweet time getting his glove, a ball, a catcher, and then casually walk to the bullpen mound as if he might be needed in 30 minutes. I need you 5 minutes ago! Move it!
You don't have to be 100% when leaving the pen. Remember, you get 8 more warm-up pitches when you enter the game. Don't keep throwing just because the coach hasn't called on you yet. Quickly get to about 90% ready and then stop. Don't worry about getting all your pitches to be perfect. Just quickly get your arm loose and get a "feel" for your pitches and command. You can fine tune when you get your 8 warm-up pitches on the field.
Throw from the stretch. This may seem obvious but it constantly amazes me how many times I see an opposing relief pitcher getting loose in the pen by pitching in the wind-up. That's a tell-tale sign of a pitcher being completely clueless of the situation he will be walking into.
Go with your best stuff. If you enter in the middle of an inning, especially in a jam, go primarily with your two best pitches. If you are going to get beat, have them beat your best. You are open to a lot of criticism if you give up runs on your 4th or 5th best pitch. If you start an inning, all your pitches are fair game.