Ask in person when standing in front of the finished work, then send the review link by text before leaving the driveway. Waiting until evening roughly halves response rates. A short automatic request two days later catches the rest.
Reviews are the single most valuable free asset a handyman can build. They feed the local map results that produce most of the work, and they answer the homeowner's real question, which is whether you will actually show up and finish.
The method that works is almost entirely about timing:
On what to ask for, encourage specifics. A review that names the repair carries far more weight with the next customer than one that says great work, and it also mentions the service terms people search for.
If you are starting from nothing, work through your last ten customers this week. Twenty reviews changes local visibility more than any other action available to you.
The Handyman BrandPack is ready to use, fully customizable, and done for you, so you get all the marketing assets you need.