Park at Housesteads Roman Fort. There is ample good parking which is charged by the hour up to a maximum of £10 a day. If you explore the fort and do this walk the parking will cost you £5 (at the time of writing 2020)
The Roman site is managed by English Heritage, you will need to be a member or pay to access the fort and museum, if you are just doing the walk then parking is all you will need to pay for.
(S/E) From the car park, enter through the English Heritage building and then follow the good path uphill to the museum and fort. (Explore the fort if you are doing that) Then make your way to the west gate of the fort.
(1) Pick up the path which runs west and passes through two stone walls. Then head up to the wall itself and follow a path past a milecastle 37 and continue to a dip at the end of Cuddy's Crags.
(2) The path slants down left and back right (or you can scramble directly down the rocky steps; the rock is polished so take care in the wet). From the dip ascend and follow the wall to where it bends south west with a magnificent view over to Crag Lough. Descend to farm buildings on the right and a way-marked gate.
(3) Turn right and go through the gate and past the farm. Go through another gate and down the track to a third gate where the path splits. Continue straight on following a grassy track which bears rightwards to a wooden marker post.
(4) From the wooden post keep on bearing rightward and head for the corner of a prominent stand of trees. Walk past these with the plantation on your right and then continue across the field to what looks like the end of a dry stone wall. (The path underfoot on this section is vague but the route is easy to find)
(5) The wall is actually the end of a disused lime kiln. Continue heading along the path which becomes easier to follow, pass through a gate or over a stile into the next field where the Pennine Way branches off to the left. Continue on the same track until a section which has been churned by the tractor. Head up and towards a stand of trees with an obvious gate.
(6) Go through the gate and follow the path through the trees, then through a second gate and follow the grassy path eastwards to an obvious stile where Hadrian's Wall dips.
(7) Cross the stile, turn right and head uphill with Hadrian's Wall on your right again. Follow the path beside the wall to a place where it goes through some trees.
(8) At the end of the trees you can climb up and walk along a section of the wall or go over a stone stile and walk with the wall on your right, passing the remains of a gatehouse. Then follow the path up beside the west wall of the fort and rejoin the good trackback to the car park.(S/E)