Hiya KellyLC,
I would take the following combined approach:
1) Use social share plugin/script - there are many out there which will hide some of your content unless the reader uses the social share feature in order to unlock view content... This is a great way to get traffic - all of which is organic and free! With the more shares you gain the more visitors will arrive and hopefully you may even get some valuable backlinks...
2) I would also approach related sites and offer guest articles... This will help with your rankings and also with traffic from the website... For really authoritative sites you may have to offer cash..
3) In addition consider use of infographics with providing an embed code below it... That will encourage people to embed the infograph and in turn providing backlinks...
4) You should also consider building your own PBN (private blog network) with buying and resurrecting old domains which can provide a nice source of backlinks..
5) Also adopt video marketing - upload videos on various video sharing sites e.g. here is a tutorial on subject xyz... I would also incorporate embedded "how to" videos to the website as that can help with lowering bounce rates...
6) Go on related forums... Use your sig link or if you are allowed mention that you have an article which solves a particular problem...
7) Join various social networking groups, participate and provide value... You can use that to provide links to useful content which solves problems... similar to forums noting that you should read the rules when joining wrt self promo etc..
8) Consider email marketing with building a list... This will help with building enduring traffic which does not rely on search engines...
9) Another great way to get backlinks is to locate links on a site which results in a 404 error (linked page does not exist)... You can use various tools - for me I use Xenu which is free... Once located contact the web owner to inform that the link does not exist with recommending your link instead...
10) The most obvious is to actually pay for links... Contact web owners and offer cash... although G is clearly against such practices that does not stop people... Just be careful on the type of website i.e. it is not an obvious one with regards to paid links...
Note: Some of the above will only give you nofollow links but you will still get traffic... In order to rank on the SERPs you will need quality dofollow backlinks the best sources for that in my opinion is through guest articles or PBNs... Personally I prefer PBNs as my #1 source of link building....
Best of Luck,
Sid