When using a Tank destroyer, be sure to hide behind bushes(Not in them), because they provide concealment and camouflage your tank so you're not spotted right off the bat. But they can still spot you by using your tracers(shots), so be prepared to move to a new spot. Also, destroyed tanks, both friendly and enemy provide good cover and so does rocks and most buildings.
The worst enemies for TDs tends to be artillery and fast-moving light tanks like the T-50, A-20, and ETC. For Light tanks, if they move quick enough and get close enough to you, they can either circle strafe around you(Move in circles around you while firing) or stop you from turning by getting close to your side, if they can't get close enough to you, they'll just let the artillery(Long-Range tanks that tend to stay at their team's base and fire using a special view that allows them to see the battle from a bird's eye view and do massive damage if they hit you or close to you, but suffer in close quarters combat) kill you for them. Best way to avoid getting killed by Light Tanks is be sure you have reliable teammates supporting you and avoiding situations where you can circle strafed easily. For artillery, just find cover behind tall rocks and buildings, it'll protecting from arty coming a certain direction, but not all and try to kill scouting tanks quickly before they can spot you.
Also if you get to a tank like the T-28 or M3 Lee, don't use it like a normal medium, use it as sniping tank.
Best place to get information on the tanks and the tank types would be the Tankopedia or the World of Tanks Wikia: