The manual, or somewhere inside the unit, will be a wiring diagram; the manual will have a troubleshooting guide. If you don't have one, you may find one on the manufacturer's website.
One of the interlocks or sensors may need to be cleaned or replaced. It sounds like the flame sensor is not detecting the burner is coming on. This could be dirty, misaligned, or not working. The leads could be corroded or loose. Lots of possibilities.
If the circulator pump is not turning on, the water inside the heat exchanger could be getting too hot, and that's shutting it down. Depending on where your temperature gauges are, you may or may not be able to see that.