The car club that I'm affiliated with has the Poker Run down to a science. Like other here have said you need to prevent cheating. What they came up with is an envelope system. First get regular letter sized envelopes and have the numbers 1-52 printed around the edge. Next you make up a paper (cut to fit inside the envelope) with the 52 cards randomly printed around the edge of the paper. When you put the paper into the envelope the cards on the paper line up with the numbers on the envelope. When you "draw a card" at the stop someone punches a hole through the envelope and the paper inside. At the final stop you open the envelope and reveal you hand.
Now that you have the idea I'll fill in the details.
For the envelope, print you numbers inside of a circle. You want to give the person running the stop an aiming point for the hole punch. Also use the center of the envelope as a place for the person's name, registration number, phone number, etc.
The slip of paper obviously has to be one sided, you can get three slips of paper out of an 8.5x11 sheet of paper. First make sure you randomize the cards printed on the paper. Next place a square, circle, or 'X' on what would be directly under the circle on the envelope. (When the hole is punched you want something to make it clear what card was drawn.) Put the card to the inside of your marker. You don't need anything fancy here, 4D and QH are clearly 4 of diamonds, and queen of hearts.
When you stuff the envelops, you have 4 ways of inserting the paper; normal, upside down, face down and normal, and face down and upside down. This is what really randomizes the cards. When you do this any number now has the chance of being 4 different cards. Make sure you seal the envelops.
To draw cards, they have 52 ping pong balls with the numbers 1-52 on them. The night before the balls are randomly split up put into 5 different bags. Each stop gets a bag. (Their Poker runs are typically 300-500 cars so each stop gets two bags. If you are going to do this, make sure the bags at a stop have the same numbered balls. You don't want someone drawing the same number at different stops.)
For a 6th card, just have a bag with 52 balls in it. If they draw a number already punched, have them draw again.
Make sure you are manning the final stop where the envelopes are opened. After you tell them their hand, put it back in the envelope and keep it. This way you can go back and look when someone claims to have a better hand than the winner. This is why you put their name, registration, and phone number on it. Any opened envelops are automatically disqualified.
After that all you need is a good course, and nice weather.