Any registered account can post on topics. There are only 2 rules: 1, you need to follow that topic and 2, you may only post once every 5 minutes, due to the 5-minute cooldown we have in place.
There are also two main ways you can post on topics.
First, by sharing content already available on Sharesome. You can do this by selecting the Share button and then Share in a Topic. A familiar posting box will show up, along with an additional field for Topics. This will open up and help you select a fitting topic for the post you wanted. Click the Post (or Queue, if you're on cooldown) button and it's done!
The second way is by creating a post. Open up the posting box, add in the content you want, then select the "Post in a topic" button and select a good one for your post. Select the Post (again, or Queue) button and the post will get created.
These features are available from many different pages on Sharesome, so explore around topics and profiles!