How do I connect two monitors to my MacBook Pro M1?

There are three versions of the M1 chip: M1 Max, M1 Pro, and M1. If you have the base M1 chip, that only supports one external display.

MacBook Pro (13-inch, M1, 2020) - Technical Specifications - Apple Support

The M1 Pro supports two, the M1 Max supports four.

MacBook Pro (14-inch, 2021) - Technical Specifications - Apple Support

Your tag line says that you have a 13" MacBook Pro. That one has a plain M1 chip and supports a maximum of one external display.

The Apple standard for its built-in hardware-accelerated displays, makes them suitable for full-motion video for production/display of cinema-quality video with NO dropped frames, and NO dropouts or partial-blank scan lines due to memory under-runs or other issues. This requires a hardware rasterizer/display-generator for each fully-accelerated display, supported by Huge memory bandwidth to refresh each display 60 or more times a second. 

If you need more hardware-accelerated displays than the built-in and ONE external display, and an un-accelerated iPad if desired, you probably need a more capable computer.

You can also have one additional less-capable Apple display using Sidecar, limited to an iPad or or Apple-TV device, but that is NOT a hardware accelerated display.