Use the recommended thinners & solvents to clean equipment, some one-pot varnishes clean up in mineral turps. Some polyurethane varnishes are water soluble, a huge saving & also reduction in environmental damage; some use acetone. However, the more exotic products will need the specialised thinners. In all cases, clean up before they begin to set. Disposable rollers & brushes may be simply left to harden & thrown into the rubbish bin. Do not dump liquid varnishes into drains or water.
Leave finished cans & mixed two pot liquids open to set & then, when hard, dispose in the rubbish. If any clothing has been contaminated, remove it immediately & wash the affected skin thoroughly with soap & water. If you have been careful then there should not be too much to clean off. Wash in soap & water; never use the supplied thinners to clean skin (they are worse than the varnish). Hand cleaners work well for most varnishes & vinegar seems to work on epoxy resins.