The third trimester begins at 28 weeks. Movements usually keep building until about 32 weeks, and this is when US guidance suggests starting to time them.
What's changing
Movements should gradually increase and get stronger until you're about 32 weeks pregnant (Tommy's, RCOG). Your baby still has sleep periods of mostly 20 to 40 minutes, when they usually won't move (RCOG).
Counting from 28 weeks
Start timing ten movements (ACOG · Count the Kicks): Count the Kicks advises starting at 28 weeks, timing how long ten movements take, around the same time each day, and comparing each count with your own earlier ones. It notes that this is what ACOG recommends.
Know your baby's pattern (RCOG · NHS · Tommy's): There's no set number of movements you should feel, and you don't need to count them (NHS). RCOG says there isn't enough evidence to recommend the routine use of a movement chart.
Both come back to the same thing: your own baby's pattern, and acting fast when it changes. How to count walks through a count.
What happens when you call, from 28 weeks
RCOG describes it: you'll be asked about your baby's movements and have an antenatal check-up that includes checking your baby's heartbeat. Your baby's heart rate is usually monitored for at least 20 minutes, and an ultrasound scan may be arranged.
If movements slow down or change, contact your midwife, doctor or maternity unit now, even in the middle of the night. If it happens again, call again, every time (RCOG).