The first issue with disposal of any chemical product is to determine if there are any legal restrictions on such disposal. That is typically included as info in the MSDS, (the SDS, Safety Data Sheet). You should at least review the MSDS for any chemicals that you use to be certain of the minimum safety requirements and the recommended safe use guidelines.
In an institutional laboratory setting, the institution (school or whatever) should provide for appropriate disposal of chemicals. That is their legal responsibility, and they will also have someone that is a point of reference (the person you can ask) for any questions about safe storage, use, and disposal. That is their LEGAL obligation. Whatever you do in their laboratories is approved by them by definition.
Corrosives that are only hazardous because of their corrosive nature can be addressed by neutralization and dilution (converted to a non-corrosive aqueous solution that can be disposed as water). I assume that chlorosulfonic acid fits this category; that is, you can dispose of it just as you would HCl or sulfuric acid. If you somehow got some base metals in there, though, that could be an issue, although not usually a practical concern because of the small amounts involved (water and air emissions tend to have both a maximum concentration limit and a total mass per unit time limit).
In a household setting, you are legally responsible for proper disposal of chemicals. There is some variation in how such products are collected, depending on where you live, but where I live, we have both a regional collection center where you can drop off the products (batteries, mercury bulbs, waste solvents, etc.), and many stores have drop-off of certain hazardous waste materials (like waste oil is accepted by garages and waste paints at hardware stores, those sorts of things). Anything that cannot go in the landfill has to go to such a recuperation center where they sort and dispose in bulk.
There was a time when we pretty much did whatever we wanted with these things, but those times are long gone.