What is the best way to get more traffic for a website, forum posting or blog comment?
High authority blogs that get a lot of visitors and updated frequently can bring a lot of traffic to your site, as much as high traffic forums can bring you a lot of traffic. I would say do them both and see what works well for you and your business.
All I'm saying is that there's no best way, both will work fine, depending on how you tackle them.
I have read various sources saying that linking in signature is best way to increase backlinks and traffic to your website as each time you comment on a forum thread. Is this true?
It's partly true, not all forums allow dofollow links in the signature so those won't count as a backlink, but might bring you a lot of traffic. Forum backlinks don't carry a lot of weight either and in most cases it won't help you rank. Don't use forums for backlink purposes, use it for traffic, networking, helping people, getting help etc.
If so, so how can I do it correctly?
That's a good question, and in my opinion. You simply have to offer value and help people. In a forum situation, you want to place your link in the signature and help forum members with their questions. Don't focus on creating too many posts, instead only answer questions that you have more knowledge about, anything that is related to what you're promoting. In that case you can be able to focus on other forums, blog and other marketing strategies.
You can even strike a deal with a highly active forum member to put your link in their signature, maybe for a commission or monthly payment or whatever deal you both agree on. Connect with members of the forum especially the admin and the mods, if you're stuff is really good and it works, then the admin and mods can help you spread the word, but make sure you add some value to the forum first before asking for any favors. Unless if the forum already has a marketplace then you can simply place your offer there and scale from there.
Same process applies to blog commenting, you simply have to add value in the comment sections. But it doesn't have to stop there, you can also answer questions left by other blog readers. It doesn't have to stop there either, keep adding value, replying to other comments (not just questions but maybe someone who's just posting misinformation etc.), connecting with the blog reader/followers and the blog owner. Each time the blog owner replies to your comments you get closer and closer to them and might end up getting a guest posting gig.
So what you need to do is to join high traffic forums in your niche and get a list of frequently updated high traffic blogs (do both forum posting & blog commenting). Visit these sites daily and add value, do this each day and as you keep posting you need to track which sites are bringing you the results you want (you can use google analytics), then filter out anything that is wasting your time and focus on what's bringing positive results.
Hope that helps