if i have a web site of web design and web development and i put my link on the footer of the page in the site which is not relevent to my business should this effect my site ranking or not.
Nebiu have a negative effect, although it is always better to keep the relevant links. I watch that is not a link to Los neighborhood.
If you had like a thousand links from unrelated sites, than yes, it would affect your rankings, and most unfavorably. If it's just one link, it's not going to hurt you in any possible way (providing it's not a bad neighborhood site). However, I can't see ec23's point: do you mean an outbound link can raise this particular site in search engine results?
Logically speaking you can not control if somebody links to you wether it's relative or not so my answer for this is your ranking will not affect.
I always say just make it nofollow. Then at least Google will not follow the link. I have seen that work for some people.
All do follow links count. If they will not help, then the worst thing that can happen is that, Google will ignore such links. There is no negative affect of getting links from other sites. I personally think that, such links will help; links are not relevant so the help will not be much, but something is better than nothing.