Of course, everyone's mileage varies, but...
When it comes to the tarp UNDERNEATH a tent, the general rule of thumb is to keep it entirely tucked under the tent. Usually none of it should extend outside the edge of the tent, otherwise you risk rain landing on the tarp and seeping under the tent. It's often better to have a separate mat for wiping feet, taking off shoes, etc.
As for the tarp ABOVE a tent, the tips about keeping it tight and keeping it angled are right on. Most modern tents -- especially the popular inexpensive, larger "dome" style tents by Coleman, Eddie Bauer, etc., have accompanying rain flies which are put on as part of the tent set up. (I'm a big fan of the Eddie Bauer series that have clear plastic windows in the rain fly that line up with the air vents in the top of the dome, making it possible to lay in the tent and look up at the stars, while still being protected by both a tent roof and a rain fly.) In settings where heavy rain is likely, it's still advantageous to string up another tarp to direct water way from the tent -- just be sure it is VERY taught and angled enough to prevent it from flapping in the wind and from water pooling up on it (nothing is worse than a saggy, sloppy, rain-filled tarp lurking above your sleeping place!).
One last tip: You get what you pay for. Thin tarps are usually cheaper, but it's often worth it to pay the higher price for a thicker tarp. They're much more durable, will withstand storms and fray less, have better grommets for running rope cord along the edges and tying up to trees, etc. Sales at camping supply stores are good bets, as are army surplus stores.