I have been playing Manager Mode in Fifa 10 (PC) for 3 seasons, however the Team Chemistry rating keep getting stuck at 60 while the other ratings (Fans Support and Job Security) are at 99.
Make sure you include training days on your roster. Chemistry comes from the players getting used to each other, so the more exposure they have to each other, the more chemistry will develop.
Player happiness also affects chemistry. If you hire an EPL player to play on an MLS team, chances are he won't be happy because he won't be playing in a league that his skills demand. Paying the salary they deserve also helps their happiness. Benched players are also unhappy so consider loaning them out -- especially if they are young, inexperienced players.
Essentially, look for ways to raise morale and get the players to know each other.
Also, putting your players in their desired position helps with "formation chemistry". Keep your right backs at right back, your strikers at striker and they'll be happier players. This might only apply to the Ultimate Team pack though, which I don't think is available on PC.
I am at Team Chemistry 66 after two seasons. I think for this you have to stick with the same set of players and keep your transfers at a minimum. You can achieve this in the long term by recruiting as many young players as you can. This way you will not need fresh transfers and same set of players will remain there for long time.