OK First advice:
If you start a game and find yourself in a corner, RESTART THE GAME! If you are next to the wall and do not have some great resources on your homeworld, restart. The mid and late game advantages from being in the middle are just that great.
The things to do on the first turn are:
Begin researching Planetary Improvements (the best overall improvement tech in the entire game!)
Buy you Capitol world a basic factory the first turn.
Send your colony ship back to you homeworld and put 500 colonists on it! Otherwise you entire expansion is slowed down dramatically.
Go to the shipyard screen and upgrade the colony ship design and add another engine.
Set your flagship for auto-explore (the A button)
Launch your colony ship and send it to the nearest star. AFTER it moves, upgrade it to your new colony design.
Set your production slider in the domestic policy tab to 100% and adjust your tax rate until your Morale is at 50%.
Begin building another colony ship.
After this read some of the other posts for advice. What you do on the first turn affects the rest of the game dramatically. The game works on an exponential scale, so small changes at the beginning have a HUGE effect later.