Open the battery compartment. Check that the batteries are the right way round and touching the metal connectors. Press "Play" on the Walkman; if the components inside don't move, then insert new batteries. If the Walkman still doesn't work, then there is probably an electrical problem, in which case you should take it to your local electronics store.
Press "Eject" on your Walkman so that the tape compartment opens. Spray the compartment with compressed air to remove the dust that may have built up there.
Insert the cleaning tape into your Walkman. Close the compartment and press "Play"; the cleaning tape will remove any dirt that has built up in the interior and on the tape heads of your Walkman.
Remove your headphones and the microphone from their sockets. Spray compressed air into these sockets to remove any dust buildup.
Dampen a cotton swab with a little anhydrous isopropyl alcohol. Open the Walkman and locate the heads (the silver metal features at the bottom of the cassette dock). Rub the heads gently with the swab, then dry with a clean swab.
Locate the capstan (the metal spindle on the right-hand side of the heads). Press "Play" so that the capstan spins. Dampen another cotton bud with some anhydrous isopropyl alcohol and hold gently on the capstan to clean. Dry with a clean cotton swab when finished.
Find the pinch roller, which is the black rubber roller that guides the tape. Rotate the roller manually while wiping with a dampened swab. Wipe the stationary plastic and metal guideposts. Dry all parts with a clean cotton swab when finished.
Insert a tape into your Walkman to test if it works; if there are still problems after following all these steps, then take your Walkman to a electric repair store so that an expert can look at it.