Spider plants are super easy to propagate in 2 ways. Firstly by division if your plant has started growing another 'twin' plant and the other is by using the 'spiderettes' that grow from your plant.
My plant was actually a gift from my mum a few months ago (aww) that she propagated from a spiderette herself! That means it's not really old enough or big enough to develop spiderettes yet but it did seemingly overnight morph into two separate plants. It was also getting a bit heavy and leaning too far out so it was definitely time for a change.
I've found that when you have 2 plants in the same pot (especially a small pot) they fight for the nutrients and generally, only one survives so it's important to split them up when they get big enough.
To do this, I first took the whole plant out of the pot and shook out the loose soil so I could see what I was working with. It was clear that the plants were separate but their roots were very entwined.
It took a bit of patience, levering and untwining to separate the plants. Some roots were torn or broken but as long as you've still got a good root base intact, some casualties are OK.
I then separated the plants into two separate pots, not too big so not to shock them, with fresh compost and a good watering.
They're such a good starter plant and the fact that you can make multiple little plants from just one is really rewarding!