While this is not exhaustive, hopefully it’s still instructive…
Tags are great. Imagine you’re building houses.
You could have groups for the customers you’re building for. Inside each customer you could have groups for each house with notes on each thing of interest. Framing, cabinetry, electrical, plumbing, etc.
You could tag each document about a construction step with the vendors involved. Documents about framing could be tagged for each lumberyard supplying materials, the carpenters doing the job, etc.
When you want to see where you stand, you might want to look at notes for a project, so you would go to the group for the customer and dive into the subgroup for a particular house. Maybe you see an order for carpet is overdue, and that note is tagged with XYZ Carpet, Inc.
Use “reveal tag” to link over to everything XYZ Carpet is doing for you. While you’re there, you might want to add a note about Moe Howard’s home needing more padding on the walls. You’re in a tag, not a group, but they are almost the same thing. Go ahead and add the note while you’re in the tag.
The new document will have the tag and the document itself will go into the database’s inbox, ready for you to move to whatever group you want.
Tags are very, very, cool. You could do the same thing with additional groups and replicants, but it would be more work and more error prone.
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The way I think about tags is this:
What are other contexts where I might want to see a document again?
So for instance you have a CRM which you dump all sorts of material in a client group/folder (email, call notes, excel documents, presentations, preparatory notes, debriefs etc) and list them in chronological order. That’s a great overview of activity.
But what if I have 2 or more different projects with the client? There are times when I want to just see the material associated with those projects. That’s where tags come in useful: tag material with project names.
What if I wanted to see all my “Meeting Notes” only? Add a “meeting notes” tag on top of the “project” tag. You could certainly perform a search instead, but tags not only makes it easier/faster, you can favourite a tag so you have that grouping always within reach. (Ok, you could save a search in the form of a smart group in DT3, that just shows how powerful and flexible this tool is.)
Of course, you could organise it the other way around: Have everything dumped into a Project group/folder, and tag who the clients or participants are.
Tags go deeper - you can actually tag groups as well! So you could tag a group/folder where you have all your dumped client files according to where along the sales funnel they are: prospect, negotiations, contract. Then later, you can see all your different clients in each of those stages. (And yes, you can also set reminders for groups to ping you when it’s time to contact someone, but that’s not a tags thing… 
.)
BTW, DT3 allows multiple words separated by spaces as tags – no need to to camel case or join words by hyphens/underscores!
It’s really easy to enter tags in the editor, or even just a selected item(s) from a list with no editor open: just use <Control-Enter>.
I use a structured process to tagging, assisted by an applescript
All notes get a type tag, selected from a list;
examples; !Type-Receipt, !Type-Action, !Type-Event
The type, drives additional tags
examples !Type-Receipt gets !Vendor and !Budget tags
Tags are structured using a a prefix to reflect hierarchy
First character is a special character ?!@.# (Who What Where When Action)
Other examples #Action-Goal, #Action-Project, #Action-ProjectNote, #Action-Task