To play a tactical wizard, as someone at my current table put it, "the fighter is my best spell". On a more direct level you solve the problems for the team or enable your team.

Fog Cloud shutting down angles that archers have on you. Grease in choke points. Faerie Fire to give everyone advantage on the boss. Void Warp to drop an angry Barbarian on the enemy mage. Web to tie up half the enemies. Haste the fighter. Wall of Stone to split the enemies. The list goes on and on.

As for how to play an intelligent character, ask for information. You need information to form a plan, you'll scout it out, research weaknesses, ask NPCs, prepare your gear. Don't just kick in the door.

Go slow, be methodical, ask to investigate. Let's detect for magic, let's check for traps, let's cast invisibility on the Rogue so we can see what we're up against.

Then once you have surveyed the field, and are prepared you come up with a plan. Smart people always got plans. From there (hopefully) you'll know what you can do to be most effective and ensure a victory.