Sure... There are different ways so I'll give you a quick run down...
The Quickest (ads):
1) Develop a simple landing page with an email opt-in stating sign-up to get this valuable report on x,y,z which allows you to solve problems a,b,c.... Make it clear that they can opt out at anytime and that the email addresses will never be shared... Next create a FB ad which targets your audience based on metrics such as age, gender, interests etc.... BTW - dont use Adwords as the info harvesting policy will stop you and you'll get your account suspended.... Instead of FB you can also use ads on related websites/forums etc...
The Organic Approach:
2)Write a number of detailed articles - I call these pillar articles relating to your niche... These articles provide great value with helping your audience... On your website place a email signup form e.g. top right column or use a timed pop-up or exit capture... Either case make sure to tell them to sign up to your list and in return they get this great helpful report....
3) Also promote your signup page on Youtube as well as social sharing sites, twitter etc...
Email Campaign:
Once you have the leads - write an autoresponder sequence... where you are helping and providing value but at a subtle point promoting your affiliate product e.g.
day 1: Here is your free report... Click this link (goes to hidden link on your site in order to get report)...
day 2: Hope you enjoyed reading the report... Let me know if you have any questions... Blah, blah... By the way I have this great tip on X and you can read about it here... (link to your site)...
day 4: Talk about another pain point and provide another tip...
day 7: Check out this --> your article review on affiliate product... Tell them the benefits and why its a great product...
day 9: Provide some more useful advice...
day 10: Tell them some more info on affiliate product and why it has helped a lot of people... you can even be upfront and tell them you'll get a small commission should they choose to access it via your link....
... etc... (give some gaps between days here and there as you dont want to over do it)...
Basically your autoresponder sequence needs to provide value whilst at the same time not being to over the top with trying to sell stuff.... If you do it in a subtle way by means of recommending it and outlining benefits then that is sufficient... Keep your emails short and provide links to articles on your site which have the details.... You may want to consider having these pages as hidden ones (thats what I do so that you keep them guessing and plus you let them know its exclusive info for your newsletter recipients only)....
Another approach could be to offer a quick training course e.g. 7 day course -- day 1 learn this, day 2 another topic.... day 7 - if you want to learn more then recommend this.....
With writing your report - you need to look at the pain points and just tackle a few of them.... e.g. lets say you are promoting the following products:
1) Acne - free report on why herbal remedies works
2) DIY - free report on how to build your own shed
3) Dieting - free report on the best juicing recipes
4) Gaming - free report hightlighting the top 3 cheats....
etc
I hope that helps! Let me know if you have any more questions and good luck ;-)