How a local crew fixes it
The fix depends on where the water comes from. Most jobs use one or more of these.
Interior drain and sump pump
This is the most common fix for Rochester basements. The crew opens a strip of floor along the walls. They lay a drain pipe in stone, then patch the floor. The drain carries water to a sump pump, and the pump sends it outside. Water that gets to the wall has a path out before it reaches the floor.
Outside waterproofing
The crew digs down along the outside of the wall. They clean it, seal it with a waterproof coating, and add a drain at the footing. This costs more and tears up the yard. It can make sense for a finished basement or a wall that needs work outside anyway.
Crack sealing
Single leaking cracks in poured walls can often be sealed with foam or epoxy. This is a small job. It is a good fit when one crack is the only problem. See foundation crack repair.
Gutters, downspouts and grading
Sometimes the fix starts outside. Downspouts that dump next to the house can soak one corner all spring. Extending them and sloping the yard away from the house can cut the water a lot. A good inspector will say so when that is enough.
Floor drain and backup protection
In the city, backups through floor drains are a sewer problem, not a wall problem. A licensed plumber can cap the drain or add a valve that helps. If you have both problems, the waterproofing crew and the plumber can work together.