How to fix braking problem
Possible issues (probably not a complete list - things I've seen)

Dirty rims - if the rim does not provide a consistent friction surface (there is dirt that makes one part too sticky or too slick - brake pad residue etc.) you will not get smooth braking.
Dents or blips in the rim - if the rim is wider or dented in some places it will affect braking smoothness.
Dirty brake pads - may not affect smooth braking but clean pads will improve general braking.

I'm sure others will have suggestions.