One direct route (interesting introduction to London drivers):-
R out of station (heading South-East).
L onto Euston Road (NE)
SO onto Pentonville Road
L at Angel onto Upper St
R onto Islington Green / Essex Road
R at big crossroads onto Balls Pond Road
L at big crossroads onto A10 (Stoke Newington Road)
Straight on for miles and miles
After Severn Sisters and just after Bruce Grove railway station, SO on A1010 (the A10 bears left)
SO for more and more miles along the soul-less Hertford Road.
Bypass Waltham Cross on the not so nice bypass (R at roundabout before high street, 1st exit at big roundabout)
3rd exit (R) at next roundabout (B176 signposted Turnford)
SO mini roundabouts under railway by Theobalds Grove
SO (2nd Exit) at next major roundabout in Cheshunt but very shortly R (Signposted Cheshunt Station).
Weeeeeee down the little hill (that you'll be climbing up at the start of LEL)
YH is right near the station.
It's about 15 miles, note that I'm a fan of directish routes along busy roads rather than sulking off to the backstreets.
There's a path alongside the canal from somewhere in London, but I've never used it and don't know how to get on to it. Hopefully someone will document that option for you.
There's also a route along the A503 through Camden, Holloway and South Tottenham but I'm not familiar with those roads.
The laziest option, by far, is to walk the bike over to Euston Square tube station and get the circle line to Liverpool St station. From there you can get a train straight to Cheshunt.