(2-part post):
As Ethel says, almost every ISP comes with some free webspace.
If, for the sake of example, your ISP is called Some Internet Firm, and your log-in is 'happyface', the web address would probably be something like www.someinternetfirm.com/users/happyface. If you only want your family to use it, that might be fine. (They'll only have to type it in once and then save it to their bookmarks). If, however, you want your own distinctive web address, you'll have to buy a domain name, such as www.happyface.co.uk. ( Although I've referred to 'buying' a domain name, in reality you actually 'rent' it. It will cost a few pounds for, typically, two year's use). You can have your site actually located, for free, at www.someinternetfirm.com/users/happyface, with vistors to www.happyface.co.uk automatically being re-directed to your site.
If your ISP doesn't offer free webspace (or you can't work out how to use it), there are various alternatives. If you Google 'free web space', you'll find loads of firms which offer you exactly that. The only problem with most of them, though, is that they'll find some way of including advertising on your site. (e.g. with pop-ups or ads which float over your site). For some people that's not a problem but you should be aware that a few of these firms carry advertising for 'adult' websites.