I have noticed that a lot of mediawiki-based websites use such templates as Robelbox, Ambox etc. Where can I get them and how should they be installed?
It's a PITA and unfortunately (unlike extensions or media files) there is no repository of canned templates. Templates load other templates which load others in turn, etc.
Go to Wikipedia and copy the name of the template you're after, go to Special:Export and paste the name of the template in the big text box, e.g. Template:Infobox. Check "Include templates" and check "Include only the current revision, not the full history", (or the file will be too big). Click Export to dump a .xml file of the template. Then import this into the destination wiki.
After it has been imported open the template for editing, check the list below the edit box "Pages transcluded onto the current version of this page:". If there are any red links repeat the above steps for these templates as well. You might also need to copy styles in MediaWiki:Common.css page and Javascript in MediaWiki:Common.js before everything works. Finally edit the templates to customize for your wiki.
If it still doesn't work and you have messy pages of braces and if statements, then you need to install the ParserFunctions extension. If there is {{#invoke: }}
in template code you'll also need to install the Scribunto extension.
MediaWiki Help:Templates explains the process in more detail.