By bus
Public transport is not reliable, though they have fixed price from one destination to other destinations.
Small minivans called sudako or angkot by locals have painted numbers 1 to 267 in Medan that signify their routes, which even locals don't have memorized. If you speak Indonesian, just ask where people are standing by the roadsides which "bus" number corresponds to your location and what the price is in advance. When a van with the appropriate number approaches, flag them down as they don't make scheduled stops just drive along a given route and drop off passengers when told or pick up new passengers when flagged. If you are a westerner, be sure to confirm the price before getting in. This type of transportation should only be braved by those with a point-to-point knowledge of Medan and a working knowledge of Indonesian so they know where to tell the driver to stop, unless you have a local friend who can take you around. Standard fee is now Rp 3,000/trip.
One easy route is Minibus #3 from the great mosque at the side of yuki mall to the Medan Mall, which is Rp 2,000.
By Becak
Also known as trishaws or pedicabs. You have to be good negotiator if you want to ride on becaks, with price ranging between Rp 5,000-10,000 depending on the destination near or far.
Very few becak drivers speak more than a few words of English, but a map and lots of pointing will get you to the right place, even if it takes twice as long as you thought.
As you can get a hotel taxi for Rp 35,000 to almost anywhere in Medan, paying more than Rp 15,000 for a longer ride is probably not a good idea. Local taxis are now Rp 30,000 to almost anywhere. They will not bargain much with visitors.