How Much Will it Cost?
Any amount you like...
You can get a blog for free if you like. However, as with anything else, you get what you pay for, and there's no free lunch.
All blogging systems are looking to turn a profit, and anything "free" is just a free sample, to lure you in the door. There's no free way to get a blog that has a proper .com domain name. This issue feeds into a larger problem for beginner bloggers.
You can never leave
Blogs are rarely transferrable from one system to another. Occasionally it's easy. Sometimes it's possible but highly technical.
Whatever system you start your blog in, is likely where it will stay. If you think blogging is going to be something you might stick with, then you should be prepared to pay a small amount to start your blog in one of the better systems. A huge number of mid-level bloggers have to grapple with this problem. The system they chose was easy at first but had hidden costs, or they've fallen foul of the editorial constraints of their provider, or they've run up against some other restriction.