Changing one out varies by the brand. Some are quite easy, some more involved. Finding one that's an exact replacement may mean you don't have to change anything except the motor assembly. But, this requires both electrical, mechanical, and plumbing skills as the new one generally won't have a power cord on it, and you'll need to do that as well.
If it's one made by ISE, you don't have to change out the sink drain and the whole thing comes off fairly easily after loosening the screws, loosening the cam lock, and removing the circular split ring.
Drain cleaning chemicals often don't work and can be a major problem if you then need to take the pipes apart as they are caustic. Chemical burns or destroying tools can be an issue and a plumber may end up charging more because you did this.