There are many themes for Jekyll, e.g. https://github.com/jekyll/jekyll/wiki/Themes.
What is the easiest way to switch to a new theme in an EXISTING Jekyll installation?
While you could migrate to an existing installation by forking a new theme and then manually copy and pasting over resources like CSS, JS, HTML in the _includes, _layouts and other files you may need, this probably isn't a great idea as you end up having a mash up of old and new resources, which may not be of the same name, but in the scenario that they are (for example you didn't overwrite an old stylesheet that your post references), it will cause mixed up CSS styles that you'll have to debug and slowly fix.
Since I'm assuming you have a Jekyll install with Git (if you don't you really should), you could create a branch called new-theme and switch to that branch from the master as the working branch. (A simpleton way of having something like this is to just copy your entire Jekyll install and paste it elsewhere as old-Jekyll-install if you don't want to deal with Git branches (but really, you should. Here's a tutorial that helped me learn)
_posts and your customized changes. _config.yml by manually comparing them and moving over what is necessary.<br \> tags for spacing and you don't want that in the new theme).master (or push it to production)That being said all this is fairly manual and a pain, but at least you won't have to deal with conflicts in resources. The downside of doing this though is that your repository won't be synced with the theme repo. So you won't get upstream updates. I would still suggest that you fork the theme repo, port over your personal customizations for your Jekyll site, and then rename that repo for production. (this would of course no longer be using the 'existing' Jekyll installation)