You'll need sharp loppers and possibly a sturdy hand saw, depending on the size of the tree or shrub. Not all trees produce suckers. Lop off each sprout back to the branch, leaving just a bit of wood on the branch. This cut thins the tree or bush, allows light to reach the innermost leaves and increases air circulation. Sometimes it is necessary to remove a branch completely, as larger branches compete with small ones, leaving the latter weak and targets for disease.
Crowded branches can also allow moisture to accumulate, creating the perfect environment for rot.
Branches that cross and rub against each other can cause wounds, leaving the tree susceptible to disease. Remove the bulk of the branch to get rid of excess weight, which could cause the bark to tear from the final cut. The next cut is the most important because if you don't do it right you can kill the tree. Leave a small piece of the branch attached to the trunk rather than make the cut flush to the trunk. In time the collar will grow a callus and heal.