Grand taxis are useful for points north and east. There are frequent taxis heading to Tan Tan (3 hours) and Smara (2 hours), fewer going to Goulimime (5 hours...if things look a bit slow, try going to Tan Tan and changing there), some land rovers going to remote outposts in the desert (as a foreigner, i doubt you'd be allowed to travel on these), and lots going to Dakhla (9 hours...ouch!) and Boujdour (3 hours) in the south. Try not to arrive at lunchtime, as nobody wants to travel at that time...early morning is busier.
Grand taxis are fine for shortish journeys, but 5 hours crushed in a taxi to Goulimime with five other passengers just about finished me off. They're great for getting to know people, and my taxi was full of big characters...two larger than life Sahraoui women ranted away in Hassaniya about all sorts of things, engaging in banter with two soldiers on the ills of the army, the occupation and bad husbands, always ending in hysterical laughter from everyone. The laughter didn't make me feel any less crushed though.
The grand taxi station (gare routiere or mahattat at-takaasi) is west of town, past the UN compound in an area called Ejercito. Take a petit taxi, or if your luggage isn't too heavy, walk downhill from Av Mekka al Mukarrama and turn right, asking for directions on the way.
You can reach Laayoune by bus from Agadir (11 hours) and Marrakesh (15 hours), with buses stopping in Inezgane, Tiznit, Goulimime and Tan Tan. Coming from the south, buses from Dakhla take just over 9 hours, passing through Boujdour.
Getting on a bus in Laayoune is a bit more complicated. All the buses originate in either Agadir/Marrakesh or in Dakhla, so it all depends how many spaces are available once the bus gets to Laayoune, meaning you can't reserve tickets. When a bus arrives, there is generally a bunfight between potential passengers, all clamouring and waving money at the bus officials, while luggage is weighed and labelled. Passengers getting off are trying to find their bags, while other passengers wander off in search of toilets, tea and cigarettes, and the bus conductor runs around trying to keep everyone within sight. I don't know why it has to be so chaotic, as surely in the age of mobile phones, someone could call ahead to say how many spaces are free, so tickets could go on sale before the bus pulls up....but obviously that's far too complicated.
If you're heading south from Laayoune, make sure you have your passport handy, and be prepared to jump off at the many police checkpoints en route to answer questions about your mother's maiden name, your profession, your nationality, your reason for being there and your favourite breakfast cereal. Some travellers suggest printing out a document with all this info on, but I tried that and still got hauled off the bus for the same questions, so there really doesn't seem any need. The police at the checkpoints are usually polite and friendly, happy to see a foreigner, especially one who can chat in Arabic or French...if you're polite and friendly in return, you'll have no problems.
CTM and SATAS offices are on Av Mekka al Mukarrama 9the main street), SAT and Nejmat as-Sahra (buses to Tarfaya) are opposite, close to the Hotel Nagjir. the only one that isn't handy is the Supratours bus office, which is out at Place Oum Saad.