I have always been a bit intimidated by bloggers' talk of "Trackback" and "Pingback", and am still unsure of whether they really do anything that isn't just as easy to do "by hand".
I recently came across a Tutorial written a couple of years ago by Teli Adlam which helped me to what I think is a bot better understanding but still leaves me wondering whether I am missing something.
When reading A-Blog you can always comment directly (if comments are permitted) and and, so long as A-Blog actually allows links in comments, you can include a link to YourBlog (preferably to a related post) .
And if you don't yet have a relevant post to link to you can always make one and then go back to A-Blog and make a comment linking to it.
So far as I can tell, Trackback and Pingback are just ways to shortcut this process by having your blogging tool send a link to your post as a comment to the one you were reading on A-Blog.
If a Trackback url or link is displayed after the post in A-Blog, then if your blogging tool supports trackback it will provide a location for you to paste a copy of that url when you publish your new post.
Alternatively, if both A-Blog and yours support Pingback (and, in particular, this is true of WordPress), then just including a link to the A-Blog posting in yours will cause your system to send an excerpt from your post and a link back to it as a comment to A-Blog - with result very similar to that of a Trackback. An advantage of this is that it doesn't require the extra step of copying a special url. Disadvantages include perhaps less control of what is excerpted (apparently it is always the paragraph containing the link), and lack of an easy way to determine if it will work. If a blog posting includes a trackback link then presumably trackback will work, and if it is a WordPress blog then pingback will also work (so long as you are also using WordPress and have set your blog to send pings).
The Tutorial by Teli Adlam that I mentioned above shows (among other things) how to tell if a WordPress blog posting will accept pingbacks, but unfortunately this seems to require checking the html source code of the page rather than being readily apparent. This makes it hard for me to see the value of relying on Pingbacks rather than just going back and making a comment with a link back to my own posting.