I used to have a simple map on this page, but let's be honest - you can do a lot better with an offcial Nevada state road map. But if you're nostalgic here's a link to my old map.
These directions start in downtown Las Vegas, NV and assume you have a car. Any size will do, as the roads are excellent, although some are gravel roads. If you're adventurous and want to get "off road" to some of the surrounding places of interest, such as Tikaboo Peak, you'll need a vehicle with high ground clearance and possibly 4 wheel drive.
Start the trip by traveling northeast on U.S. Interstate Highway 15 toward Salt Lake City, UT. At a distance of 23 miles from downtown Las Vegas, take the exit to U.S. Highway 93. Cross under the Interstate and go north on U.S. 93 for 93 miles to the intersection with Nevada Highway 375. You'll pass through the town of Alamo at 81 miles and Ash Springs at 88. Check your gas gauge; there's no fuel available in the direction you're going.
Turn left on Highway 375, the "E.T. Highway", and keep to the left where Highway 318 veers off to the right. In 12 miles you'll be at the top of Hancock Summit. Another 3 miles along Highway 375 brings you to Groom Lake Road. It's gravel, but well maintained and no problem for any vehicle. You can drive down this road for 13.8 miles but no further. The numerous, large and threatening signs will tell you when you've arrived at the Area 51 border. Don't cross it. The border is marked by orange posts and it runs diagonally across the road.
The town of Rachel is 25 miles further on Highway 375. Stop for a meal at the Little A'Le'Inn. It's the best, and only, place in town to get a meal.
All mileages are from the Official Nevada Highway Map and my notes, except for the distance down Groom Lake Road, which is from Glenn Campbell's " Area 51 Viewers Guide". (No longer available.)