Busses are lousy and get stuck in traffic jams like everyone else;Trains only connect Jakarta with the outside world;There is no such thing like a subway, tram or monorail;So the best option is a taxi.
Taxis are cheap an ubiquitous. There are reports of robbery by taxi drivers, so some basic care is necessary:- The blue "Bluebird" taxi's are ok, as are their more expensive black "Silverbird" cousins. Watch out: there are numerous Bluebird lookalikes: same type of car, same colour, only with a different logo.- Ordering a taxi beforehand by phone is a safe way too.
During rush hour, taxis can be difficult to get hold of. When it's raining, the traffic jams are such a nightmare that getting a taxi can take ages, and getting to your destination with it even more...
An average taxi ride will cost you between 15,000 and 50,000 rupiah IDR = between 1.2 and 4 USD.
Walking is not an option. Jakarta is simply too big for it + as soon as you leave the hotel, restaurant, shopping mall or office building "enclaves", you end up in dirty streets where everybody stares at you if you don't look Indonesian. Nobody speaks English and proper signs are non-existent.
Trains are a good alternative to get out of the city, e.g. to Bogor.