Move Your Blog from WordPress.com to WordPress.org
So you have been using WordPress.com for quite some time now and things are great so far. But, it came to a point that you wanted to go beyond what it could offer like customizing your theme and installing plugins. With this, moving to WordPress.org site is an excellent move.
Export WordPress.com Content
Log-in to your WordPress.com account
Scroll down to the bottom.
Install WordPress Importer on your New Self-Hosted Site
Go to the Dashboard of your New WordPress site (self-hosted)
Check the box ‘Download and import file attachments‘. With this, images and other attachments from WordPress.com will be imported.
Check your New WordPress Site if it contains the posts/articles from your WordPress.com site.
Redirect Users to your New Domain
Free WordPress Site
If you move your blog without informing your readers or visitors, you will certainly lose them. The best way to deal with this issue is creating a new post informing readers about the moving of your site to a new self-hosted domain. Be sure that you add a link pointing to your new site in your post.
Paid WordPress.com Site
For paid WordPress.com site, site owners have access to plugins to help them so the redirect could be done automatically. The redirect plugin will tell search engines that the site they are trying to access has been permanently moved to a new site/domain. With this, SEO strength of the previous site will be transferred to the new site.
Here is a video on different plugins to use for the redirect