I can't tell if its Opuntia or Notocactus, pic's not clear or bright enough,but general rules for care are:- average warmth spring to autumn, cooler in winter (10-15 deg C), in the sunniest spot available, specially in winter, don't leave on a cold windowsill overnight in winter. An open window nearby for fresh airflow is useful, and from autumn onwards, reduce watering, so that over winter, its only given just enough to stop it shrivelling. From spring, increase watering, such that by summer you're treating as a normal houseplant, which is, water well when the surface of the compost feels just dry to the touch. Use tepid water. Repot annually when young, preferably in spring - if its too crowded in its current pot, you can do it now, but only use a pot one size bigger.

Definitely not an Opuntia. There are several very similar looking ones but I think it looks more like an Echinocactus than a Notocactus. Does it need repotting - yes it does but wait until spring unless you can do it within the next week or two. . Use cactus compost which nowadays you can buy ready mixed thank goodness. Tip the plant out onto your hand (wear thick gloves or use several layers of newspaper) Check that there are no patches of white stuff clinging to the pot or the roots. Use a new pot that will give you about three quarters of an inch clear all the way round and repot to the same depth it is now. It is a good idea to finish with a layer of coarse grit to make sure the body of the plant does not stay in contact with the soil when it is damp.
Do not water it for a week or two to give it time to settle. Underwatering is no problem so err always n the dry side. Water from the bottom and never let it stand in water afterwards. In winter a little once a month is enough, but when the weather warms up you can give it one good soak. There after once a fortnight should be enough unless the weather is very hot. Just remember its designed to live in desert conditions.
Giver ot a quarter turn every few days to prevent it leaning over to the window and keep it in the sunniest place you have. Deserts can be very cold at night so as long as it doesn't go below the mid forties it will be fine.

Sorry Bamboo, got a bit carried away there...

All true! Just for the record, it's Echinocactus grusonii. I would repot it when the sides touch the pot, like it is now. Note that barrel cacti use water so slowly that you may only be watering it once a month indoors, even in the summer. When you repot, use a very sharp draining compost. Growth and color will be improved if you feed it 1/4 strength tomato food, about every third watering, once the nutrients in the compost have faded. In time, and with good conditions, it will grow to about a meter tall, and 70 cm wide--in maybe 40 years!

I really hoped it was grusonii. I used to want a big one when I was in my teens but never splaahed out as they are very expensive! I do now have (I hope)a small one which I got as a seedling, about twice as big as the one in the pic, but have never been confident that's what it is.
Even Hywel couldn't be sure...