If operated upon for cataract, can i see properly thereafter?

If it goes well: And the eye is healthy otherwise, should reach expected visual outcome after healing.

If all else is well!: The purpose of cataract surgery is to remove the clouded lens from the eye and to replace it with a new one, thereby restoring vision. If all the other structures of the eye are normal, it is likely the vision can be fully restored often without the need for glasses!

Yes: Vision usually decreases with cataract formation; Depending on pre-operative risk factors (ie, hypertension, diabetes, pseudoexfoliation, trauma, etc) the vast majority of patients achieve 20/20 vision after cataract surgery (low risk factor patients). Most patients say colors are brighter after surgery & VA much better. More info at: eyedoc2020 blogspot com

Usually: If the eye behind the cataract is normal, and the surgery goes without complications (the usual case) then you will see well within days. If there are problems in the eye with things like diabetic retinopathy, or trauma, etc. then the vision might not improve so much. Ask the ophthalmologsit what is likely in your case.