The nearest station is Watford High Street, a ten minute walk away from the ground. However you are likely to come into Watford Junction train station, which is about a 20 minute walk. Either get a train to Watford High Street from Watford Junction or if you have time to walk to the ground then:
Leave the station & take main road straight opposite (Clarendon Road) all the way (over Ring Road at lights) up to the High Street. Turn left and go past past Wetherspoons (Moon under Water) on your right and then take the first right after 100 yards into Market Street. Continue along again crossing Ring Road to T junction & then left at an excellent chip shop. Vicarage Road is the next right turn. Should take around 15-20 minutes to walk.
Watford also has its own London Underground tube station, which is on the Metropolitan Line and is situated just under one mile from Vicarage Road. However overland trains from London normally have a shorter journey time.
There's one about a mile away from the ground if I remember correctly, the journey back was such a drag though but I think there may have been works on the line so we may have had to go a different route.