Highgate is in zone 3 for ticketing and Archway is in zone 2/3. The stations are both on the Northern Line - the Northern Line is a complicated line for tourists because it has two destinations High Barnet and Edgware. If you are going to Highgate or Archway on the Underground you need to be on the High Barnet branch. If you are taking a Northern Line train out of central London and you are on a Edgware train simply change at Camden Town to a High Barnet bound train.
However do bear in mind (see other tips here) that both Highgate and Archway stations are quite some distance from Highgate village.
The best way to travel to Highgate village is by bus - the walk from Highgate or Archway tube stations is up very steep streets and quite a long way (as I found out!) - there are not even any signs at Highgate station to direct you to the village.
Take bus 210 - Golders Green to Finsbury Park / 143 Archway to Brent Cross / 214 Liverpool Street to Highgate Village / 603 Swiss Cottage to Muswell Hill / 210 Brent Cross to Finsbury Park.
If you need to take the Underground take it to Archway - have a look at the Whittington Stone (see my tip) and then take a 143 or 210 and get off in Highgate village near Pond Square.