Reblogging is when a blogger posts another Tumblr's entry. This can be all or part of an entry. Tumblr says:
Reblogging lets you quickly share things you find on Tumblr. Clicking the Reblog button next to any post will create a copy on your blog, and give you a chance to include your own comments.
Reblogged posts automatically include attribution to the original poster.
Liking an entry is showing support of an entry. If you like an entry, your Tumblr name will be listed on the entry you liked.
How to Reblog (From Your Dashboard): Each post list the number of notes, a reblog link, and a heart in the top right corner. If you click REBLOG, you can reblog that entry. You can see the link below. (It's slightly darker than the other links.)
You can also visit the entry (on its own, not just the blogger's main page) and click REBLOG. It's in the top right corner:
How to Like (From Your Dashboard): Following the directions above, click the HEART.
OR visit the entry and click the heart:
...And that's it.