This page covers a few basic 3-way junctions. Only block signals will be used here, although you can improve the junctions by using Path Signals. The junctions are optimised for the use with the "Realistic acceleration" setting enabled. If you have fast and long trains which use the junction, you might need to make the curves a bit wider, so that the trains don't have to slow down.
The very basic 3-way junction
This junction is fast & easy to build, and will not cost much money. However, due to the block signals being used, only one train at a time will be able to use it. If you have only very few trains running on those tracks you won't have any problems, but as soon as the traffic density increases, your trains will start jamming in front of the junction.
A little improvement...
With this setup, you can improve the throughput of your junction quite a lot, since two trains driving on the parallel tracks going from the upper left to the lower right corner can use it simultaneously. However, if a train from the uppermost track wants to turn left, and a train coming from the lower left corner also wants to turn left, they will still block each other. Building a bridge instead of a tunnel would of course work the same, but remember that tunnels have no speed limits!
Advanced 3-Way Junction
To improve the junction a bit further, we build a second tunnel and a bridge and ensure, that tracks always split before they merge, and that tracks do not cross each other. The junction now works quite good and is already suited for moderate traffic. However, if two trains coming from the upper left corner are driving very close behind each other, and both want to go straight along the line, the second one will have to wait before the tunnel, since we do not have signals on bridges. On the regular track, the signal distance is always 2 tiles, but with the tunnel, it is temporarily increased to 5 tiles.
Advanced 3-Way-Junction with doubled briges
To prevent jams caused by the scenario described above, we can build two parallel bridges or tunnels, instead of just one. The second train can then use the second bridge/tunnel and does not have to wait in front of a red signal.