I want to install SSL certificate for my website which is hosted on a DO VPS. There is a "free" SSL guide which I am not able to get results with.
Which Free Tutorial you are talking about ?? As there are two I guess, one Self Singed another is free from StartSSL..
Free self singed will always generate warning but the StartSSL given SSL is browser valid certificate.. If you are facing issue about the same, better to discuss in that StartSSL tutorial as comment to get further help for installation..
But there are a lot of options to choose a SSL provider. Which provider should I buy the SSL from (bigger problem) and how should I install the certificates into my VPS?
The problem actually is not from who you should buy, rather what should you buy ??
There are many category, starting down from,
DV or domain validation only.. Cheapest
Wild Card (which helps to validate every subdomain) SSL
Company validation
then comes the Extended Validation for that complete Green Bar with company name on visitors browser..
Installation process may vary deepening on your back end, for example, I am running a control panel, CentOS Web Panel, so my installation process would be bit different than plain no panel apache host..
Where as expensive panels like cPanel installation can be done with few clicks..
a free ssl cert from startssl would be a good first try. You can always replace it with a purchased ssl one.
The free one from startssl will not have warnings if you set it up properly.
If you are asking for a recommendation which SSL is good at affordable price, then I would go for NameCheap website because they offer RapidSSL at $10.95/year. so if you have a coupon/discount then you make get it a lot cheaper especially if you make a long term purchase say 2 years minimum.
For the installation procedure, I believe they 'RapidSSL company' explain at their site how to install it. it is very simple and doesn't take more than 15 minutes.