Determining the origin of an oil leak can be tricky. Place some cardboard or ideally white paper or sheets on the ground beneath the engine area. The colour of the oil leak will help you to work out where it's coming from. Engine oil will usually be black. If the drops are directly under the engine, it's engine oil. A slow leak follows ribs on the engine block, is blown along the top of gasket joints, and oil gets everywhere. You may need a good source of light to check this. 

If it is an engine leak, it does need to be attended to. A leak can affect oil levels and if not checked can do internal engine damage. Replacing a gasket can be expensive so you don't want to go replacing one unnecessarily.  It probably would be worth while getting it checked by a professional - or a mate if you know anyone who knows a bit about auto mechanics.

Eventually all vehicles will start dripping.  Some brands start earlier than others...I'm sure you've heard the joke about British cars: "British cars don't leak oil, they just mark their territory".

Since you have not indicated the amount of oil that is leaking, we'll start with that.  A drop or two overnight probably isn't a big deal.  If it looks like the Exxon Valdez paid a visit to your garage floor last night, then it's a much larger issue.

If the spots on the floor are black (or brown if the oil is fresh), you know the leak is limited to the confines of the engine.  What this means is that the oil has to be coming from somwhere between the timing cover and the rear main seal (front to back) and from the valve covers to the oil pan (top to bottom).  You haven't indicated what type of car this is, but we'll assume you have a standard "wet-sump" engine, rather that a dry-sump (a big oil tank) sports car like a Porsche 911 or Corvette ZR1.

The easiest thing to do is simply run a paper towel around the most common problem areas.  Valve covers tend to weep over time and are the easiest to see, so start there.  If the area below the valve cover(s) are clean, chances are the leak will be from the oil pan or rear main seal.

This means jacking the car up.  Always use jack stands for safety! Slide underneath and inspect the oil pan.  First look at the drain plug in the oil pan.  If it is wet with oil, this is an easy fix -- go to a parts store and buy a new one for a buck or two.  Next look around the edges of the pan for leaks.  This is a common area of failure over time.  If there is a bunch of oil leaking out, you'll need a new pan gasket, which is usually a pretty easy fix.

If valve covers and oil pan are clean, then look to where the engine meets the transmission.  These seals are notorious for leaking, especially in cars before the 1980s.  If it's wet here, the fix is generally much more complicated -- requiring much time and effort to get between the engine and transmission, so unless the oil leak is severe, you might just want to do routine checks on your oil level to ensure there's always sufficient oil in the engine.

Some important notes:

If the fluid is red, look for leaks from the transmission.

If the fluid is green, it's coolant.  Check for leaks in the radiator, hoses (cracked hoses or loose hose clamps), and at the sides of the engine heads, which would indicate head gasket failure.

If the fluid is yellowish and appears near the wheels or from under the master cylinder, this might be brake fluid.  Get professional service FAST otherwise you might find the car has no brakes.

And a good tip:

If you're still having trouble finding the leak, it might be because the engine bay and underside are too dirty/oily to isolate a single leaking area.  Use some degreaser, a brush and towels to wipe metal and plastic areas clean.  Never soak wires or connectors, and keep water/soap out of carburetors and air filters.

 

I've had the same problem. I parked on a clean public highway (no mess on my drive) and left it there for 24 hours. Then I moved the car along the street and worked out where the leak was coming from (front, middle, back, left/right?) from the stain on the tarmac.

me either. i was on the highway when one of the part of my car got busted. and there i tried to fixed it. fortunately i have the equipments so i easily trouble shoot my car. and actually i had just order parts from autoparts.com that time and had just brought the parts.