I have created a small video on do follow and no follow backlinks. the video will show you how to tell the difference betwenn the 2 types of backlinks.
In short do follow backlinks get followed by google and authority will be filtered down to your site – this is the best kind of backlink to go for.
No follow backlinks have a special code on them telling the search engines not to pass authority to the backlink.
I would still recommend using no follow backlinks as they make your offsite seo look natural and they still hold some good value. I previously ran a test on No follow backlnks by using yahoo answers which only give no follow backlinks. the results were amazing and this is the reason why i would encourage all of my readers to still go for no follow backlinks especially when they are coming from high page rank domains.