There are many laundrettes scattered around Taipei, most of which are self-service but also many offering a pick-up service.
These laudrettes have both washers and driers available. They only tend to take NT$10 coins, so be sure you take plenty. They do usually have change machines that take NT$100 notes however.
Most (but not all) will have detergent disposal machines also. These normally cost NT$10 per sachet. They sometimes have softeners for the same price.
The prices for using the washers vary from NT$40 – NT$120 – depending on size and location. The driers cost around NT$10 per 6 minutes.
To use the washing machine, just put your clothes in, pour in detergent via the latch at the top, insert your NT$10 coins and press the start button. Some washing machines may also have a few settings but you can just use the default one.
They’ll normally take around 30 minutes for a full cycle.
The driers are also fairly simple to use. Insert a coin and press the button to the right, ensuring you select the one corresponding to the location of the machine (in this case, yellow for the top drier, blue for the bottom)
Keep inserting coins, ensuring you press the same button after each coin.
The temperature can be changed by selecting one of the three buttons with the light. Left-most is high, middle is medium, right-most is low.
You can use Google Translate with camera mode selected to verify the settings if necessary.
30 – 40 minutes is usually enough to dry your clothes on the high setting.
There are also handy baskets available to help you move you washing.