Heimerdinger might be the greatest dps and the best turret defence char out there. Beside this he has the ability to have a presence more than one place on the battlefield with his turrets (favoring the choice of boots of mobility). The downside is the lack of ability to focus and control his dmg output and his fragility to other champions attacks making him hard to win with 1 vs. 1.

All this will favoir a special role for him, that can be exremely usefull to the team.
Initialy he will often be mid, where he might score no kills, but also fight relatively safe 1 vs. 1 and slowly damaging the enemy turret while should he need to healing his own teams turret. The key here is to learn to not rush things too much.
After the initial phase (somewhere around lvl 10ish) he will secure that waves of minions attack top and bottom giving the opposing team the choice between tieing up champions to defend or slowly loosing top and bot turrets while the battle is going on elsewhere. Heimerdinger does this very effectively since he can leave turrets to start the waves and run to other tasks. It's easy to learn.
He will be the insurrence dude that will take up a relatively strong 1 man defence should the rest of the team have an unlucky fight where most or all of them die.
He will often when top and bot waves are doing there job be a good addition to the battle forming a base with his turrets and figthing from the back of the team.
All this is suplemented with his unique ability to heal damaged turrets (slowly)!

Good luck and have fun with this unique champion.