You will want to travel to Moorgate station if it is open, or otherwise to Bank. You are aiming for the junction of Moorgate and London Wall.
The stairs that take you up to the 'Highwalk' are round the side of Moor House, facing on to London Wall. Head up the stairs, and continue round the building where you should see 'Moorfields Highwalk' and the escalator exit from Moorgate tube. This part is pretty rundown; it gets more interesting in 5 minutes or so - keep the faith.
Cross the square, then walk on Moorfields Highwalk under two buildings, keeping to the left. Cross the footbridge, go under the next building, and you'll see the space age architecture of the Barbican in front of you.Bus transport near Moorgate.