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Some chemicals are harsh, so put on gloves to protect your skin. Don't pick a sponge that's too abrasive, such as steel wool. Stick with a scrubbing sponge. Otherwise, you may take the finish off your tub. Additionally, it's helpful to use a toothbrush or grout brush to get into the nooks and crannies, as well as around the faucets. Magic Erasers or similar products can be perfect for acrylic bathtubs which scratch easily. Magic erasers are relatively inexpensive and can be bought from local hardware stores or supermarkets. All you need to do to use one is wet the eraser, scrub the tub, and rinse well afterwards. You have many options available to you. Which one you choose depends on your preference. For instance, you could use Lysol Bathroom Cleaner, Clorox Clean-Up, or Scrubbing Bubbles. Each cleaner is a little bit different. For it to be the most effective, you need to follow what the instructions say. For instance, you may need to spray or scrub a solution on and leave it for a period of time.  Bathroom cleaners can be quite overpowering so make sure the room is well-ventilated and if necessary, leave the room for a time to prevent inhaling any dangerous fumes. Products such as Scrubbing Bubbles Mega Shower Cleaner are meant to deep clean your shower once a month. To use, apply the product to the tub and walls. Leave it on for 3 minutes. Wash away the product.
Put on gloves. Choose a sponge and brush. Pick a cleaning product. Read the manufacturer's instructions. Use a once-a-month cleaner.