Wear moisture wicking running gear if possible. Moisture wicking socks are especially important.
If it's cold as well as rainy, wear layers, plus a hat and gloves.
A rainy day is likely to be dull, so reflective gear is recommendable.
Watch out for puddles. They might be concealing pot holes.
Beware of extra slippery surfaces. The white lines on the road are more slippery than the black asphalt.
Once home, place newspaper in your trainers. It'll absorb the water and help them retain their shape. You might need to replace the newspaper a couple of times.
Finally, enjoy! A run in the rain can be refreshing, invigorating and exhilarating!