In my experience there are three steps:
1. Install/Update SSL Certificate
2. Amend htaccess file
3. Amend all urls to relative and amend all urls to https
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1. Install/Update SSL Certificate
You can buy a certificate or get one for free. I use sslforfree.com. This means I have to update the certificate more regular than a paid for certificate. The installation can be done from within your hosting package normally. I use cpanel.
2. Amend htaccess file
Put this at the very top of your htaccess file: This is what I use on my website.
If you don't get 'secure' in the address field in your browser it will probably be because you need to make all url's relative and not absolute.
DirectoryIndex index.php
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
3. Amend all urls to relative and amend all urls to https
Self explanatory.