Pretty easy and straight forward to do. Simply go to the Time Trial option, set up your session but make sure that the weather is set to the 'Wet' option rather than dry. Select any other options as you please. Drive round the track, ensuring you don't cut corners or crash into walls. Slow and steady for 1 lap to make sure it is a clean lap, then you can push after the 1st clean lap, if you wish to attempt a good pace.
Rinse and repeat for 5 different circuits. I like to write down the circuits I have completed in my phone notes app, so I don't waste time going into a circuit, to find out I have already completed it.
This can contribute to the below achievement if you have not yet unlocked it;
The Time Flies achievement in F1 2016 worth 25 pointsSet a clean lap in Time Trial at 10 circuits