I have now gone sucker fishing two years in a row. It is generally in late April to early may and this year apparently the suckers stayed even longer. Basically, you can't really entice suckers into biting lures during that period. Because their numbers are so high and they are quite large it is fairly easy to snag them. It is however, Catch & release.
Sucker fishing is quite easy. Find a runoff creek and when they come in huge numbers cast either treble hooks or large crankbaits and it is considered easy to snag them.