The directions can be viewed by clicking the "Directions" link at the bottom of the map.
It is highly recommended that the driver or navigator prints a copy of the directions. The drive takes a little over 25 hours so driving in shifts is a good idea.
An alternative route that has been considered and should be decided on with your car is driving south to California and spending a day or two in Yosemite before continuing onto Red Rocks.
Information on camping at the state website
Some things to keep in mind are There is no running water and there are no reservations for campsites Camping for a group of up to 10 people (limit two cars) is 10 dollars per night, so roughly 10-20 bucks a person for the trip depending on how fully you pack the campsites. It can get windy. If your tent is prone to blowing away or blowing over you may end up having to spend a night or two in a hotel.
Supertopo also has a few suggestions.
Check the food & water (it's a desert you know !) subsection in Supertopo's Stayting in Red Rocks section.
Supertopo's website has a comprehensive page dedicated to climbing at Red Rocks, including a +100 list of climbs (not all detailed) and a free copy of the Black Orpheus (large PDF file) section from their Red Rocks book (including a map of the park)
What to bring
Bring American money and a passport. You will get hosed on the exchange rate if you try and use a debit card. Bring your climbing gear, camping gear (reasonably warm), and a guide book (at least a photo copy). Travel Insurance you do not want to try the American Health system without this, as you may have to trade a kidney for bandages