Most of the time the turbulence we experience is termed "chop", which is akin to what you experience on a boat on the lake -- bumps but no real altitude deviations. With altitude deviations we'll call it "turbulence". Within these broad categories we'll qualify them with "light", "moderate", "severe" and "extreme" in reports to ATC and other aircraft. These reports do suffer from a fair bit of subjectivity with respect to aircraft type (wing stiffness) and pilot experience.
If it is light chop, I'll generally just ride it out and turn the seatbelt signs on.
The first thing I'll do if encountering moderate chop or turbulence is to query ATC and get ride reports from aircraft ahead of us and at different altitudes than us. From this information I'll make a determination to ride it out or to request a climb/descent. If the turbulence was particularly bad, slowing down was an option, but I only came across that need a few times. Our ability to descend would often be limited by route length and fuel and major lateral deviations also depended on contingency fuel, so in some cases we had no choice but to stay in the chop. If the turbulent areas were well forecast or had lots of PIREPS, our dispatchers would sometimes route us differently.
As for power adjustments, if we weren't slowing down due to aircraft limitations I would just adjust power so that maximum airspeed deviations stayed below Mmo.