Reblogging is a core feature of Tumblr that doesn't really translate well to Dreamwidth. There are a couple of different ways to replicate it, but which one you pick depends on what your goal was when reblogging a particular post.

"I want to be able to refer back to this post at a later date."
The feature you want for this is likely Memories. Memories are a site-specific bookmarking system that predate tagging. In those times, a lot of LJ users would use it to organize their own posts, such as keeping track of their fics. (Tags were introduced a relatively short time before Dreamwidth split off from LiveJournal.) Memories can be public, access-locked, or private. Any Memories you make on Dreamwidth will be of Dreamwidth posts only.

Unlike with Tumblr's reblog feature, if you add someone else's post to your Memories and the original poster deletes it or locks it, you will no longer have access to it, but it does give you a way to keep track of posts made by other people.

"I want to be able to spread the word about this post."
The way most Dreamwidth users do this is by making their own post about it, either in their own journal or on a community, and including a quick blurb and a link to what you want to share. (If it's a post by another Dreamwidth user, it's considered polite to ask in the comments if OP is okay with you sharing the link around. Most people are okay with this if they made a public post, but some may ask you to make your own post about the topic instead, especially if their own post is access-locked.)

That said, there's also technically a workaround made to mimic reblogs, made by astolat (yes, that Astolat), ljwrites, and melannen. I haven't tried it myself and don't particularly want to, so there aren't a lot of questions I can answer about it. However, I would say that it would still be polite to ask for permission to reblog a post in this case, especially since, as far as I'm aware and unlike with Tumblr reblogs, the original poster will not automatically be made aware of your reblogging.

Interestingly, I've heard that this reblogging tool can also work on some non-Dreamwidth site links, such as from AO3.

"I want to share this cool, funny, or interesting thing with other people."
Did a friend or someone else you subscribe to make a post that you thought was particularly funny or insightful? I recommend sharing it at metaquotes! Metaquotes is a community specifically dedicated to sharing fun and interesting things made by other people. It's not very active at the moment, but with a little work, we can change that...

"I have something I want to add to this post."
If what you want is to share your thoughts on a topic, I recommend replying to the post with a comment! If it's something you would have put in the tags or comment section of a reblog (and isn't rude), I can about guarantee that the original poster would be interested in receiving it.

There are exceptions; if you feel like your comment might derail too much from the original post, or if you manage to exceed the character limit for one comment, you might consider making your own post (with a link to the original), and replying to the original post with a link to your own.


And those are the basics! You may want to mix-and-match on these, depending on the content and your goals for it; for example, if someone posts something really funny that you want to share, you can reply to the post, and post to Metaquotes, and link back to it in a post of your own. But overall, these options should cover most of your needs.

If you have any questions, or if there's something I missed, please feel free to let me know in the comments!