The streamers are usually crepe paper. Sometimes a tougher material called forestry tape is used, usually when it's wet out and the crepe isn't holding up in the air. (holding up to just flying around).

Streamers are cut either by the prop, or by the wing. Rules vary, but in the AMA / RCCA classes, sticky stuff is applied to the wings LE to grab the streamers. People use differnet things for sticky, everything from double sided tape to honey to tanglefoot.