Hi, I don't know too much about plants, and picked this one up second-hand. I've been watering it once a week, and giving it a little less light, but it's not very happy, so I thought I'd do a bit of research on how to best keep it. Does anyone know what sort of plant it is?

Hi and welcome!
Your plant looks like a flowering bulb called Eucomis or Pineapple Lily. It is not typically grown as a houseplant so that is probably why it appears to be declining. I suppose it is possible to grow it indoors but it would need a lot of hours of sunlight to keep it happy. In warmer climates it can be grown as a perennial, zone 7 or higher. I grow several varieties outdoors in pots for the summer then overwinter dry indoors; once light levels improve they can be started back into growth again to be put outside once the warm weather returns.
Hope this helps!

If you leave them outside, they will go dormant so maybe your's is just going dormant and will return in the spring. Follow Debbie's recommendations for winter care.

Yes, if it is a Pineapple Lily (Eucomis) it's probably going dormant.