It's important you get the what, and the when, right when answering this question so you don't end up buying cover you can't use and don't pay too much for the cover you do.
Owner-occupier or landlord?
The first question you need to answer is "Whose property is it?" If you live in a home you own - either outright or with a mortgage - then the Buildings are your responsibility and you'll need to put right anything that goes wrong with them. That's where Buildings cover comes in and insures the physical buildings - so the walls, roofs, floors, windows etc. so you're protected from financial loss should the worst happen and there be a storm, flood or fire, for example.
Normal home Buildings cover is designed for owner-occupiers, not buy-to-let, so if you own the home but don't live in it, perhaps because you rent it out, then you'll need Buildings cover but in the form of landlord insurance instead.
Assuming you're an owner-occupier, the next thing to think about before getting quotes is the contents of the home.
Contents - who do they belong to?
The next question is "who do the contents in the home belong to?" The answer to this depends on who lives in the home. Most home insurance policies will cover the belongings of the policyholder and their family that live with them. So for a household consisting of mum, dad and two kids, if mum takes out the insurance, generally speaking any contents belonging to dad and the two kids would also be covered. If it's a group of friends living together in a house or flat-share it may be more difficult to get a single policy to cover everyone's belongings, but individual 'student contents' policies might come in useful. It's worth bearing in mind though before buying student contents insurance that a lot of normal home Contents policies will include some cover for items kept away from the home at college or university, so check your parent's policy (if you're a student living away from home) before forking out for more cover which might just be duplicating cover they already have.
If I need Buildings and Contents cover, do I need separate policies?
Most home insurers will offer combined Buildings and Contents policies and this is probably the most common way for owner-occupiers to protect their home and belongings. But, sometimes circumstance might force you to have them separate. For example, your mortgage might include Buildings insurance, so you need to arrange separate Contents cover. Or you have a high amount of Contents so need bespoke cover, but your home itself doesn't warrant bespoke Buildings, so it's more economical to insure them separately. Typically you'd expect to pay less for a combined Buildings and Contents policy than you would for a Buildings only and a Contents only policy - it's cheaper for an insurer to sell you one policy than to sell and have to administer two individual policies for the same person. If a claim affects both your Buildings and Contents and you have separate policies, expect to pay an excess on both.
What if I have separate policies now?
Pretty much all insurance companies that offer Buildings cover will offer Contents cover, but not all companies that offer Contents will offer Buildings! So, if you want to combine your covers you can either add Contents to your existing Buildings cover when your Contents policy next comes up for renewal, or take out a new combined Buildings and Contents cover and cancel the separate Contents. Either way, in future you'll always have the same renewal date for both parts of your cover. Cancelling part way through the year can trigger a cancellation fee and if you've claimed you're unlikely to get any refund so check before you make any decisions though the overall saving may offset any cancellation fees.