Unfortunately that depends on your provider (domainfactory, strato, all-inkl, etc). Best is to get in contact with them and ask what steps are needed to get an SSL certificate and switch the domain to https://.
After this is done you should indeed follow Armins tutorial to switch anything http:// to https:// in your database. Otherwise some content could get lost (I’ve been there).
Don’t be afraid,… although all this may sound complicated it really is not.