Here are the basic rules for the River Teno

Updated for season 2004 - NO CHANGES FROM PREVIOUS SEASONS!:
season starts June 1st and ends August 20th
fishing licenses are 24 hours from 19.00 to 19.00 next day
no fishing from Sunday 19.00 to Monday 19.00
bank fishing only 20 €/license, bank/boat 35 €/license, upper river 10 €/license (upstream from the Matinkongas-rapids in the upper Inarinjoki-river). Additional licence for family members: 5 €/licence.
during the time from 20th of June to 20th of July the special flyfishing area in the lower Alakongas-rapids is in effect. Only 35 rods allowed. License 20 €, daily fishing hours 19.00-07.00. If more than 35 are interested there will be a daily lottery.
no fishing closer than 50 meters to mouths of such tributaries that have salmon runs (these are marked on the bank), also no fishing in the tributaries
no fishing closer than 50 meters to downstream of salmon traps or 10 meters from fixed salmon nets/traps
bank fishing fly only except at some marked spinning areas (Alaköngäs-rapids, Yläköngäs-rapids, upstream from the Matinköngas-rapids in the upper Inarinjoki-river). No additional weights allowed (=buldo etc), traditional fly tackle only
artificial bait ONLY at all areas
kelts (salmon that have stayed in river over the winter) have to be released immediately
minimum size for all fish 25 cm
boat fishing: only locally registered boat allowed; no fishing from an anchored boat or from a boat with motor running; local rower NOT mandatory between 21.00-14.00 all days except Sunday 19.00/Monday 19.00 when all fishing is closed
there are traditional rules that apply to boatfishing. It's better to ask locals how to do it or even better, hire a rower!
Complete rules & official information (PDF-documents):

Finnish: Tenoinfo

English: Tenoinfo

Swedish: Tenoinfo

To sum it up: if you fish from bank (wading) with normal fly tackle it's OK almost everywhere from Monday evening to Sunday evening.

I didn't make these up. I'm sorry that they are complicated.

The border problem: Fishing the Norwegian side

no wading across (impossible at most places)
when boat fishing only temporary stop at the other bank (coffee break etc), NO camping
for longer visits the border has to be crossed via the bridges at Karigasniemi and Utsjoki or from Nuorgam by road
for fishing from the Norwegian bank the Norwegian fishing permit is needed (from post offices) in addition to the Teno license
disinfection compulsory - certificate of disintection issued in Finland should be accepted also in Norway

REMEMBER TO DISINFECT ALL YOUR TACKLE TO PREVENT GYRODACTYLUS-PARASITE FROM REACHING TENO!

There are many new stations for disinfection - all licence outlets have now the necessary facilities.

More advice here: in english på svenska