You can view a Mastodon user's public posts with a particular hashtag by adding /tagged/(hashtag) on the end of their public URL:
(account's public URL)/tagged/(tag)
For example, @FediFollows posts with the hashtag #Art can be viewed at:
https://mastodon.online/@FediFollows/tagged/art
You can find the public URL of a Mastodon account by going to its profile and clicking on the avatar image.
You can let visitors filter your own posts with featured hashtags by going to:
Edit Profile > Featured Hashtags
Add a hashtag you want to highlight and click "Add new", or select one from the suggestions list. (You can remove tags from the list by clicking on their "Delete" buttons)
The featured tags will appear next to your public profile, people can click on them to filter your public profile by these tags.
Have you searched for a particular hashtag and not found enough results?
One trick you could try is searching for hashtags on other instances by going to this web address:
(other instance) /tags/ (hashtag without #)
For example, here are #DogsOfMastodon posts visible on the instance https://mas.to:
https://mas.to/tags/dogsofmastodon
This is useful if you are on a small/new instance, and you aren't seeing many results for tag searches.
Larger/older instances tend to have a lot more posts visible, because they have made more connections with more instances over a longer period.
Is there a way to see what posts a user boosted with a given tag?
More generally, is there a list of the special urls?