It’s amazing how many sites make it sound very tricky – but it’s really quite simple. To keep a happy sourdough starter in the fridge, feed it once a week. Mix equal parts starter and flour and also a little less water than flour. So if you have about half a cup of starter, add half a cup of flour and about 3/8ths of a cup of water. Really, that’s a very specific amount – I generally eyeball it – if it’s more or less flour than starter, that’s fine – you just want it in the same ballpark. And if you add as much water as you add flour, that’s fine, too – you’re just going to get somewhat runny starter after a while – and that’s OK!
If you have too much starter, just toss out the extra – it’s just flour & water (& yeast) – just toss it in the compost or dump it down the drain.
I generally mix it up with a fork – not worrying too much about getting it well mixed – the yeast will hunt out the flour, and the water will eventually soak everything, so there’s not much for you to do. I keep mine in a mason jar with the lid on loose. If you make it air tight, the jar WILL crack and may literally explode.
Note that I said a happy starter and once/week. I’ve left my starter unfed in the fridge for at least 3 months. If you go for a long time (2 weeks), your starter won’t be ready to use right out of the fridge, but that’s OK. If I have ‘tired’ (neglected) starter, I generally feed it and leave it out for 12 hours before using the starter – 12 hours is about a normal feeding period for starter that is not in the fridge (so you would feed starter that’s out of the fridge twice a day). After the 12 hours I use what starter I need, feed the rest, and put it back in the fridge.’