Leith is the historic port of Edinburgh. In the photo above you can see the old town surrounding the river before it enters the modern docks. The Tall Ships Races have started from this port.
To Leith from Edinburgh is about a 20 minute bus ride and there are frequent buses.
From the South and East head up the A1 into Scotland and as you get close to Edinburgh follow signs for the A199 to Leith.
From the South and West head up into Scotland on the M6 and A74(M) and when you get to Junction 13 take the A73 to Edinburgh. Once near Edinburgh follow the ring road eastward until you see signs for Leith on the A199 as above.
By Coach
Accommodation
There are lots of places to stay in Edinburgh Visit Scotland has a good local directory.