Several mini buses depart Banda Aceh for Takengon every day. While there is some sort of schedule - departing Banda Aceh at 9 am and departing Banda Aceh at 11 am, buses usually don't go until they are fairly full, so this may mean the 9 am is cancelled.
The trip, which costs 80,000 rupiah and leaves from Banda Aceh central bus terminal, takes between 8 and 9 hours. This largely depends on how many stops are made before reaching Takengon. On the trip I did, we stopped 8 times in the last hour, dropping people off in villages and sometimes taking quite long detours to drop people at their doorstep. While this was a bit frustrating, I was lucky enough to be on a mini bus with a very friendly, helpful driver and his assistant. They bought me coffee at our first stop and helped organise a meal at our lunch stop.
The initial part of the trip along the north coast road seems to go quite quickly as the roads are well made. Turning into the centre of Aceh, and heading towards the highlands, the roads are in considerable worse condition. Having said that, there is some great scenery, and at times going slow gives you the opportunity to appreciate the view.
There are plenty of becaks travelling up and down the main streets so it is easy to find transport for a trip around the lake, around town or to specific sights. I used a becak to view the lake, travel to and from Loyang Koro, around town and to the hot springs out of town. Negotiate rates beforehand. I paid 20,000 rupiah an hour - could have bargained harder if I wanted to, but it was a nice day for a carefree ride and my driver was also a good guide.