Can anyone tell me what a domestique is, also how many are on each team, and do they count in the standings for the team.

A domestique, IMHO, is really just an internal (to the team) status. Domestiques are there to support the team leader/captain. They do this by sacrificing themselves in terms of energy and standings. Some will go back and fetch waterbottles and then struggle back up to the front delivering them along the way to other teammates. Others will provide a tow so that the captain can be fresh for the endgame. Some will have the job of chasing down a break in order to either reel them back in or wear them down. There are a variety of things a domestique will do but basically they're there as riding support. They can fullfill other individual or standings roles (win stages or jersies) too as long as it doesn't conflict with the ultimate goal of the team and team captain.

A domestique is someone who like pampers the leader. (IE- Roberto Heras to Lance A.). They go back to get water/food for the leader, they draft for them, they chase down attackers. Domestiques sometimes are speciailized, like Heras is a climber. Their times are taken into account, however usually their leader is the one who is meant to be in the lead and hopefully win.

Thanks guys, also how long does a rider stay a domestique?

It's not necessarily an apprenticeship/trainee type thing. Every team has a different balance to every race. If we are taking the TdF as an example - teams tend to have climbers, sprinter and GC contenders. The term domestique literally means servant, helper. In the case of USPS you essentially have 8 helpers for one GC rider. Many of them have been specifically employed to help Armstrong win the TdF. Heras though may again try and win the Vuelta this year (after a runners-up last year).
Tyler Hamilton moved on from being a helper to Lance to a genuine GC contender at CSC.

The differences in the sprints in the first three flat stages of the
TdF compared to the stages in the Giro when Cip was contending were impressive. Cip's team has the sprint down to a fine art.
Three high speed riders give Cip a lead in in the last 4-6km of the race, with the pace accelerating to 32-35mph, one rides for 2-3km and then goes off and the next guy continues hammering for all he is worth for 1-2km and the peals off and the 3d guy takes over. Cip has 'iron shoulders' and is very difficult to dislodge from his protected position in this train. Everybody else is trying desparately to get a wheel. Finally the 3d guy peals off somewhere below 500m to go and Cip winds it up and does his stuff. Happened everytime. Wish the TdF would have some over heads of the final 5km to show the sprint tactics. The TdF sprints have been a bit more mano a mano and chaotic by comparison with Cip's well oiled machine. Steve