This depends a lot on how aggressively you apartment/house hunt. I know a few people who pay ~$350 a month/person but that is far from the norm and they tend to either be homeowners, live on the edge of town, etc. I think a more average range is usually in the neighborhood of $500-$800/mo +/- utilities. One bedrooms will be on the higher side of that range and two or three bedrooms will be on the lower end assuming you live with roommates (note I'm more unfamiliar with the cost of one bedrooms because I've always had a roommate).
If you live downtown (like Old Town Fort Collins) rent tends to be a bit higher, as well as if you look in the main housing streets right off campus that advertise to a lot of undergrads (these are usually off, like, Prospect, Elizabeth, etc on the west side of campus). The farther you're willing to live away from campus the better the housing prices will be (in general).
Something to remember too if you do want to live with roommates is that FoCo has a housing ordinance called U+2 where only 3 unrelated people can live in an apartment/house together unless the apartment/house is specifically zoned by the city to house more. Most 4+ bedroom houses aren't zoned to house 4+ unrelated people, so be careful if a landlord is trying to sell you really hard on living in a place but can't prove that many people can live there or if they try to make someone pay "under the table"/keep their name off the lease (this is relatively uncommon, but be careful regardless).
Also, a lot of people live in other towns like Loveland (bit more affordable), which is a ~20-30 something minute commute each way when the weather is good (depending on how far into Loveland you live). Sometimes if the weather is inclement the I25 will get shut down, but there are (generally) other roads to get from Loveland into FoCo.
I'm terrible at real estate hunting but I pay ~$450/month here. A lot of current veterinary students will post on class pages looking for roommates and that's how I stumbled into my current place.