Living as a pilot in a country that has >3500mm of annual rainfall and afternoon TS as frequent as 200 days per year, I would say only experience can teach you how to deal with it.
As you asked for approach and landing phase, I will share my thoughts on just that.
1) Check out the CB cloud like the way you check out the women if you can see it. Top, middle and how her skirt(curtain of rain) flares. How tall the top tells you how much vertical activities inside. How wide the middle portion tells you how much juice it has inside. How the skirt flares tell you the TS is in which stage. Straight skirt say just started,microburst is around the corner. Flare skirt says windshear/micoburst may be happening.
2) Stages of the TS tells you wind direction. Example: you're 10nm final on ILS, a TS 3nm at the runway 2 o'clock would be sucking up sh!t until it bust. Once burst, it give you a strong headwind on short final. Best to compare your spot wind at glideslope capture and tower wind. This comparison prepares you for any wind direction shift(nose cock) and wind speed change prepares for possible airspeed lost.
3) ALWAYS-go thru missed approach drills on final and commander should let you know he is ok if you elect to go-around. So, you will not feel pressured to land.
4) Good to check fuel quantity prior intercepting ILS. Alternate airport weather should have been obtained prior if fuel is not the luxury.
5) ALWAYS- Visual with runway does not mean you must land. Beware of last minute unstabilised apporach
6) ALWAYS- Water on runway takes about 15mins to drain out if runway NOT grooved. Don't rush for approach once visibility improves.
7) If runway surface is undulating, it can have multiple patches of water, antiskid can work against you. Use the reverser until taxy speed.
8) Lastly, no one likes aircraft on mud and wet grass, especially management!