By bus

Most people in Albania travel by public bus or private minibuses (called “furgons”), which depart quite frequently to destinations around Albania. Furgons have no timetable (they depart when they are full) and in addition to big cities provide access to some smaller towns where busses don’t frequently run.

Furgon stations aren’t always in obvious locations, so you can ask around to find them, or keep an eye out for groups of white or red minivans gathered together. Destination place names are generally displayed on the dashboard, prices are never posted. Furgons are loosely regulated, and provide a real “Albanian” experience.
From Tirana, many furgons a day depart to Shkoder, Durres, Elbasan, Fier and Berat. Furgons departing to the south like Sarande or Gjirokaster, tend to depart fairly early in the morning. Generally, furgons cost a little more and go a little faster, but can be uncomfortable over long distances because of the close quarters with other passangers.
Buses are more comfortable and cheaper, run on a time schedule (though it is almost impossible to find a printed schedule anywhere in the country) and are generally well regulated. Their are different bus stations in Tiran, for North bound buses (Shkoder, Leizhe, Puke…), South bound buses (Sarande, Gjirokaster, Berat, Vlora, Fier…)
One publicly-edited list of the departure locations and times of furgons and buses in Albania may be found here, but of course these should always be taken with a grain of salt!

By train

Limited services operate between Tirane e Shkodra, Fier, Ballsh, Vlora and Pogradec. The Tirana-Durres trains (and vice versa) depart up to 8 times a day. As of 2006, the trains in Albania are still in extremely poor condition – despite the route Tirana-Vlora looking convenient on a map, the more wealthy Albanians never use trains and if not travelling in their own cars, use the many mini-buses.
A train ride is a must-see, as there are few such enjoyments in Europe these days. Tickets are very cheap and the journeys are very long, but the views and the atmosphere are usually priceless. On most stations you’ll find people selling sunflower seeds, fruits, chewing gum and many other different things – very unusual in Europe.

By car

The roads between the important destinations have been recently repaved and fixed, and offer all the security measures one would expect on a highway. There are no fees for using the highways.
Beware of minor roads. Road surfaces can be poor, deeply pitted, or non-existent, and sometimes a decent paving can suddenly disappear, necessitating a U-turn and lengthy doubling-back. It seems all the expensive cars in Albania are SUVs, rather than low-slung sports cars – and for good reason. Ask the locals in advance if travelling away from a highway.
Highways have frequent changes in speed limit (sometimes with little apparent reason). And there are frequent police mobile speed checks. Police will also stop you if you have not turned on your car lights. Ensure you travel with driving licences and insurance documents (ask your car hire company for these) to present to the police.
Car-driving behaviour on the highways is not as orderly as elsewhere in Europe. Expect cars to pull out infront of you, little use of indicators, and hair-raising overtaking. Lanes on dual or triple carriageways tend to be observed.
Navigation is pretty easy although some maps of the country are out of date or contain errors.
In the cities, and especially Tirana, many roads are being upgraded and fixed. Because of that, traveling by car inside the city will be slow. Be aware that especially Tirana suffers from great traffic congestion during mornings and midday.
A very nice ride is the Vlorë-Saranda mountain road. It is a typical Mediterranean road and offers an amazing view of the sea from the mountains.
The road to the top of Dajti mountain is very bad, though does not (just about) require a 4×4.
Gypsy and beggar children may approach your car at major stop lights. Nudge slightly forward to get them off your car and if necessary go into the traffic intersection to get rid of them. The locals will understand.

By bicycle

The potholes, driving standards and lack of places to stay in many villages and towns make Albania a challenging cycling destination, but a rewarding one. Often, asking around to see if you can stay in somebody’s home / camp in their garden is the only option. Food and water are easily available in the frequent roadside cafes and bars.
It is OK to camp in all not strictly private places, and even if the places are private there should be no problems with your stay, ask if you doubt.
Be aware that it’s very hard to get parts or repairs of modern bicycles.

By hitch-hiking

Hitch-hiking is not very common in Albania. However, many people will give you a ride, if they can.

Sources: wikitravel.org