While most of southern Morocco is an arid region, if you are looking to find the "real" Sahara (rolling sand dunes with very little vegetation), you will need to travel a fair distance away from Marrakech.
The 2 closest desert areas from Marrakech are Erg Chebbi near Merzouga, and Erg Chiggaga near Mhamid. Erg Chebbi is the more popular of the 2 with travellers, given its higher, colourful dunes, though reports vary concerning the actual heights of the dunes in both places. Both of these areas are a full day's drive from Marrakech (over 500km's); keeping in mind that the speed limit on open roads in Morocco is 80km/h; 60km/h or 50km/h in towns. Expect the total 1-way driving time to these areas to be approximately 9-10 hours with limited stops.
Given the distances involved, it is recommended that the minimum required time to enjoy a desert trip from Marrakech is 4 days/3 nights. Using this plan, it will limit the amount of drive-time in 1 day to around 4-5 hours, and give you the opportunity to actually see some of the country instead of rushing thru and missing out on sights en-route. The round-trip can be done in 3 days/2 nights, however this means that 1 of the days will be a full-day drive without the chance to see anything but sights thru the window of a vehicle. A 2 day/1 night desert trip, while theoretically possible, is not recommended.
Popular overnight stopping places en-route to the desert are Ait Ben Haddou, Ouarzazate, Skoura, the Agdz area, Todra Gorge & Dades Gorge. Hotels & guesthouses can easily be found in all of these areas.
While many travellers choose to hire a tour company or car & driver for desert trips, one can easily hire a rental car and drive themselves. Once outside of Marrakech, the driving is very straightforward, with relatively little traffic, good signs (French & Arabic) and decent road conditions. The Tizi n Tichka Pass over the High Atlas Mtns. is a mountain pass with many twists and turns, but is in good condition, and should only be a potential problem in poor or winter weather.
The only part of a desert trip from Marrakech that *requires* a guide, is the actual overnight desert trek. One can hire camels or 4x4 vehicle for an overnight trip onto the dunes via organized company, local guide or desert hotel/guesthouse. Many can be found and booked online via their website/direct email.
The TripAdvisor forums have MANY of these contacts already listed by travellers, and trip reports also contain excellent info posted by those who have already been. For more detailed info from others already posted, type in key-words (eg. desert tours, desert trek, tour companies, camel trek, etc.) into the Morocco forums Search Box, and one will find many pages of excellent, specific information that has been contributed by your fellow travellers.
A desert camp generally consists of a group of semi-permanent tents, grouped together with a central eating/gathering area and (hopefully) separate toilet/outhouse. Some camps even offer running water, flush toilets and shower! Of course, facilities will vary depending on cost and services offered. Overnight treks usually leave from the edge of the dunes around sunset, and will return in the early morning light, before the heat of the day sets in. Expect to have dinner at camp, and possibly a very light breakfast as well. If you book your trek via a desert hotel, it may be possible to leave luggage in a storage area in the hotel instead of a vehicle overnight. **Be sure to ask all questions regarding services and facilities offered BEFORE you book your desert trek, so that you will not be disappointed upon arrival at camp.
Hopefully this information has been helpful to any potential desert-trekkers. I hope that others will add other useful information as time goes on as well. A Moroccan desert trek is an unforgettable experience, and I hope you have a great time!