Question: I'm currently working on my own golfing language which is based on Python 3. Once this language is finished, what would be the best way to let other people use it? I know TIO is very widespread here, and that some users' languages are on TIO - is there a way to get my language on TIO as well (and, if so, would there be an easy way to maintain my language if I wanted to add an update)?

As it stands right now, this language is far from complete (and doesn't actually have a name yet, so I'm open to suggestions). This language will get its code through a single `parse(String)` method, where `String` is the code itself.

Answer: 
Create answers written in your language
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The best way to advertise a language is to answer challenges with your language! People will eventually discover your language and start using it too. This demonstrates why is your language good and why should people use it.

Make friends with active users here by chatting in The Nineteenth Byte (*don't create your own chatroom*. That's what you'll do when your language gets at least a little bit popular. Discussion in TNB is much more likely to be noticed than discussion in a custom chatroom.) and let them use your language. Have one or two stable users other than you.
Port the Interpreter to JavaScript
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Most of the answers here don't actually answer the question of how to best make the *interpreter* accessible to everyone. So I'll add a way that opens up the programming language to easy online usage.

Here is the process I'd use to make an online interpreter (it may not be the most efficient way, but thus far, it's the only way presented)

Step 1: Create a simple user interface
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Ensure these things are present on the page:

* Code box (where the program goes)
* Input box (where the program's input goes)
* Output box (self explanatory)

Step 2: Actually translate the base interpreter to js
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Turn the program in the non-web-friendly language into js line by line.

You could look at transpilers (in this case, python to js). But make sure that it translates it properly. An example python transpiler is Transcrypt.

Step 3: Link js and html
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This is pretty simple: use things like `<script>` tags to include the js files.

And that's it. This is highly oversimplified, but it's a reasonable method of making an online interpreter.

I'd recommend hosting your interpreter on something like Github Pages (which is 100% free).