There are a number of ways you can start blogging. You can either start blogging "for free" on some of the popular blogging networks like wordpress, blogger, tumblr, you can even start a blog on your facebook profile by creating a specific page. There are lots of free options available; you can google for other platforms that suit you.
The only problem with so called free blog platforms is that you aren't always really in control of what happens or what advertising is put on it. Also if the platform decides to ban certain blog types or disappears (remember myspace?) then you have lost all your work.
Another option would be to go with your own hosted platform, this is a set up where you would register your own website and then host your own website. this puts you in complete control of your blog. Domain name registration (your website name) can be had for a couple of pounds and if you look around hosting can be found for the price of a starbucks/costa per month.
It may sound techy and difficult, but it really isn't. There are tons of good courses online that can show you. Just don't be tempted to fork out for a paying course when starting out; you really won't need it as there is tons of good stuff freely available.
Wordpress is pretty much the standard platform for self hosted blogging, it is very simple to learn, easy to use and offers plenty of options to grown if you decide to make it into something bigger. There are lots of templates available for your website free or more complicated ones for a cost.
If you already write things then you are more than half way there, you just have to get your stuff out there.
To get your blog "out there" you can create separate social media accounts linked to your blog or to you as a writer. At first it will be difficult to get traction or people to follow you, but if you publish regularly and set time aside to promote your blog eventually you will get more traction.
I write for a number of blogs and once you get into a routine it is actually quite easy and rewarding to do.
I could go on for a bit, but I hope at least this has helped you on your way.