From Guildford Station, follow the River Wey tow path south for 2 miles.
About 1/2 a mile past a railway bridge, cross a road bridge to follow the east bank of the canal. Continue, then south at the next road bridge, crossing over the Wey river to the start of the disused railway line.
Follow it - there is a short diversion at Cranleigh (houses on the line!) and a slightly longer one at Rudgwick (bypassing a closed tunnel)
At Christs Hospital (train station) there is a longer diversion where the 2 closed lines are split by a still used line. Either follow the road diversion (about 1 mile along narrow lanes with occasional fast cars - not really good for children), or continue into Christs Hospital village, and follow the pavement south to rejoin the route
The next short diversion is at Partridge Green (more houses on the line), and again at Henfield (ditto).
The railway line fades away just short of Bramber, but there is a waymarked route via fields then quiet residential streets (safe for children) to rejoin it south of the town for a final short stretch before it disappears for good. Here a handy cycle path along the River Adur starts, and takes you all the way to Shoreham-by-Sea
A road bike is OK but a moutain bike is better for the short stoney strech of path near the end.
You'll need a map for several short diversions aroud bits of built-on trackbed