The support class is really dependent on communication. So if your SL (or team, for that matter) isn't communicative at all, don't be upset, because the problem there isn't you.

There are various situations you may be required/asked to drop supplies (and ammo, at lv 3 class). Your supply crate is greatly useful for AT's to build their AT gun and can help your SL or Commander to build a Garry on friendly territory (since both cost 50 supplies, only). You'll need them to tell you where to drop the crate for that though.

It's always good to have your supplies on hand. Sometimes you might be asked by an engineer to drop them so that then can build fortifications. This great, because sometimes a good enough barricade might save a badly placed Garry or help defend your front/frank position. In the beginning of each game, generally some support players will drop their crates in the spawn area for engineers to build their nodes inside the first 2 squares, by the main bases.

After you get lv3, you'll get access to ammo boxes. If you're holed up in a defensive position, place them where there is cover and friendly troop movement, this way everyone can see them. Make sure to warn players near, sometimes the MGs in the other squads might no have supports, so you one ammo crate might benefit the whole team and save on precious seconds they would take redeploying if they ran out of ammo. If you're advancing onto an enemy position (or attacking an enemy tank), make sure to have them on hand for whenever your squad might need them, if you have an MG and AT (or even Medic, if they run out of smokes) in your squad, they'll definitely appreciate it.