Under the hood, there will be a little brightly colored ring like the back of a ring-pop (usually orange or yellow). If you pull it out it will be a long thin rod and the end should look like a little spoon/spatula. The end will have two lines on it (usually).

1. Let the car sit for a while so that the oil can drain back into the bottom of the engine/cool off.

2. Pull the dipstick out and wipe it dry with a rag or a paper towel.

3. Then put the dipstick back in and pull it out a second time. (Doing this pull/wipe/insert/pull method makes sure you're reading what the level in the pan is and not getting any oil from the tube or leftover from when the car was running.)

4. See where the oil level is. Usually the oil should be somewhere between the two lines. Also take note of the color of the oil, although that's not as important (it should be gold almost like honey, brownish is fine, black is bad, glittery = new car).

Assuming your car is roughly correct it will probably be towards the bottom of the allotted area but it shouldn't be too low.

If the oil is indeed between the two lines and not any crazy color, then you're probably fine to keep driving it until you can get the oil changed. And given that the only warning you have is the standard mileage check, you're almost assuredly fine, and I bet that 15% would last the rest of the week anyway. If you have trouble finding the dipstick, just Google "(Your car model here) dipstick location" and you should get some pictures.