une boisson = eg. We've got ten drinks to choose from. un verre = eg. I have one more drink before I leave.
it would be "coupe" if youre talking about a trophy or "tasse" if you are talking about a cup of coffe/tee Note that a Wine glass is also called "coupe"
boire un coup
drinks (noun): les boissons (he) drinks : il boit, elle boit (verb 'boire')
To have a drink with you is 'prendre un verre avec toi' in French.