Getting to Borobudur by public transport isn’t hard, if you don’t mind changing buses once and waiting at the bus station for a bit.
The first step in the journey is to get to Jobor bus station. Depending on where you are staying you can get the Trans Joga straight there, from Tugu Station there is the 2A.
From here you can catch a bus to Borobudur. We were told to get on the bus called Cemara Tunggal or Ragil Kuning. These names were clearly written on the bus, so you can’t miss it. The buses take about an hour to 90 minutes, and have fans to help you cool down…a bit.
Once at Borobudur it is a straight 10minute walk to the temple. Ask anyone and they can point you in the right direction. There is no need for a taxi or lift there, but this is offered to you as soon as you get off the bus.