Being active doesn't require any special assignment. Even ordinary members can be active.
In trade union operations, being an active member is often thought to mean that the member acts as an official in a local branch, or as a workplace shop steward or occupational safety and health representative.
A member can be active even without having a special assignment.
You can be active by, say, keeping an eye on working conditions and incidents in your workplace, and by talking with your co-workers or with the shop steward. In this way, the shop steward may get valuable information from employees to benefit his/her own work.
Participation in the union’s and local branch’s publicity stunts is part of trade union activities, too.
If you don’t wish to be involved in a long-term assignment, you can take part in short-term projects organised every now and then by your local branch, the regional offices, and the union.
More information about the topic:
Home pages of local branches (in Finnish)
Event calendar (in Finnish)