To find out if you are on the search engines just goto the search engines and type in
www.yourdomain.com or whatever and see what comes up.
As for links there are two things you can do you can check your "link popularity" online at
http://www.linkpopularitycheck.com or you can do what I do and download this very small programme which tells you how many links are going to your site and your competitors, if you input your competitors name. Its a free bit of software and you can download it from
http://www.checkyourlinkpopularity.com
That tells you how many are linked but to find out WHO is linking to you goto the online checker and click the 'details' button next to the results, this will show you all the pages that are linked to you.
Also as siphilp mentioned if you can track your visitors with a stats package that will tell you where visitors are coming from. If you dont have one you can get one from
HERE for free i use these on my site as well as a hidden one as i find this gives some info that others dont.
You can see an example on my site
HERE scroll right down to the bottom of the page and then click on the black icon in the bottom left corner
Its a good bit of kit, hope that helped