Pick up an all-day Travelcard from your local station on the day or grab one early at www.nationalrail.co.uk, plenty of services to get to the ground in time.
You can change at Stratford for a central line to Tottenham Court Road and change to the Northern Line High Barnet Branch or West Ham and the Hammersmith Line to Mile End, however there could be engineering works planned for the day, check at: www.tfl.gov.uk/tfl/livetravelnews/realtime/track.aspx?offset=weekend
You can use your Oyster card from both West Ham and Stra tford so just get day return there, or go straight to London Liverpool Street or Fenchurch Street, and then use it from the Liverpool Street underground, you could get the Central Line to Tottenham Court Road and change, or walk to Moorgate or the Bank, not worth buying one for the day.
The above tube information applies if you have purchased a Travelcard.
The nearest tube station is High Barnet which is the end of the line of that branch of the Northern Line. (Don't go to Edgware!)
There is only five minutes walk down Barnet Hill to the ground (although it is a fair hike back up the hill after the game!).
Alternatively you can take a quicker train to New Barnet railway station, which is around fifteen minutes walk away from the ground. This station is served by trains from London Kings Cross and is a shorter journey time than the tube, taking around 20 minutes from Central London.
Coming out of New Barnet station turn right and then left into Station Road. Walk up to the traffic lights opposite the Odeon Cinema and turn right onto Barnet Hill (A1000). After going under a railway bridge, you will be able to see the ground behind the Old Red Lion pub on your left.
Alternatively you can get a bus from New Barnet Station; the 84, 384 or 107 buses run every 15 minutes or so from New Barnet to Underhill.
(Thanks to www.footballgroundguide.com for stadium directions.)
Maps
High Barnet Tube: Top right; New Barnet Station: Off the map, to the right of the ground, coming in off Station Road; Underhill Stadium: Bottom right.
Remember, it's in a Group Save area that can cut fares in half if four of you can travel together, and any various travelcards will make it even cheaper.
To find out more, go here:
www.daysoutguide.co.uk/groupsave.aspx