Summarize:

Get in the habit of washing down the tub with a mild soapy cleanser and water every week. This will prevent dirt and grime from building up which would take longer to remove. Regular washing will also keep stains from forming in the acrylic tub and tile near the tub. Don't clean your acrylic tub with materials that can scratch the surface. Never use abrasive scrubbing pads or sponges. You should also avoid using steel wool which will also damage the surface. Instead, use soft cloths and sponges. For example, you could use a microfiber or terry cloth towel. You may need to use a drain cleaner or tub clog remover every once in a while. If you do pour this down your tub's drain, you'll need to rinse it away completely, so there's no cleaner or remover left standing in the drain area. If you leave cleanser or clog remover in the drain area, it could damage the acrylic surface. To avoid discoloring the tub, most acrylic tub manufacturers recommend that you never smoke in or around it. This is because tobacco smoke can permanently damage the tub.
Clean the tub out weekly. Avoid using rough sponges and cloths. Rinse the drains thoroughly. Avoid smoking around the tub.