What is the proper way to post links to your website aside from informing the owner of the website that you want to link his website and vice versa? Thanks
post the links where in blog posts, articles, Forum Signatures or somewhere else please elaborate.
What I mean is, for example I stumbled upon this site which contains information relevant to my website and I want to direct my visitors to that website if they want to know more about this information. How do I go about this?
cmveneracion, Only link to your website in sanctioned areas (as in where you are allowed to post links - such as signatures on forums), if you do link to your website in a post, ensure that it complies with any rules the host website might have (in regards to self-promotion) and if you want to make the post neutral (more likely to be accepted), post some links to alternatives (apart from yours) which are also relevant - you don’t want it to be blatant spam, but if you’re including your own link as part of a relevant discussion it might be fine. Most importantly of all, follow the rules… if they say no self-linking, no promotion, no nothing… then don’t. 
If you want to link to another website from your own website, simply add the link. The author of the other site (if they check their stats) will notice it soon enough and if he/she feels the topic of your site is relevant to theirs, they might even link back to your site.
Alternatively you could contact the author of the other site and see if they want to trade links.
Just insert then link of that site in your posts for the particular keyword and you will be able to redirect your traffic to the other site
Just add the link if it is relevant to the discussion or site. But first read and follow the rules.
Am I understanding the question correctly – you are putting a link on your site to another site? Then there are no rules, you can do whatever you want. And if you want, please link to mine