Actually there are just
bunches of ways to do this, but
chiph is correct as usual.
Either you make it all available as a download, including the database, and basically lose multiuser capability (everyone gets his own Access database locally) or else you partitiion the application into a user interface at the client and logic and data piece back at the server.
It is amazing the number of choices you have beyond this though.
I'd guess you start by deciding what your client technology is going to be. The three basic options are:
1.) HTML/DHTML page(s)
2.) ActiveX control(s) hosted within a web page
3.) Java applet
I'd rule out the latter for a whole bunch of reasons, starting with the fact you're a VB programmer.
Most everything else is some variation of those three. I haven't messed with VB web classes but I think they come down to basically option (2.) above. Same thing is true for .HTA (HTML Application) clients - this is really just a "trusted" version of (2.) that can be installed locally as an application just like an EXE and show up on the START menu.
Next you need to figure out your "glue" or wire protocol. If you're gonna call it a "web" application you're pretty much stuck with using IIS or a similar web server to host your logic (which will connect to your database). With (2.) and (3.) you could even use plain TCP sockets to get to your main ("middle tier"

logic piece - but why work so hard? This would require you to build a custom multiuser socket server, build your own security and management stuff, etc. Yecch!
So you basically use either (1.) or (2.) and communicate with an ASP application at the server via HTTP POSTs and responses. Even to use SOAP as your protocol you'd probably opt for the standard HTTP wrapper and thus end up writing ASP pages.
Now, your ASP pages can be pretty thin if you like, basically just invoking your VB code as one or more objects with one or more methods.
The upshot though is that you are looking at a major rewrite and rethink unless you built your application with this in mind in the first place. State-management is one issue, and then there is the idea of reworking your application to be transaction oriented instead of event-driven.
This is a new ballgame.
I have seen people wimp out though, and go with a 4th option. I think it is crap because it eats resources like crazy (including bandwidth).
This is the Terminal Server or Citrix-like option.
1.) You carefully adjust your VB application so that it can run on one machine multiple times under different user contexts. This doesn't have to be a HUGE deal though, but it is important.
2.) Then you host the VB application on an NT 4 Terminal Server Edition box or a Windows 2000 Advanced Server box.
3.) Get enough client licenses for all your users to connect to it.
4.) Then the users can use either the stand-alone Terminal Services client program to connect
or use the "Terminal Services Advanced Client" which is really the stand-alone client application repackaged as an ActiveX control in a web page. Then the users download the thing from a web server and you call it "web based" (yecch).
But this way the user interacts ("over the web" but not really using web technology except to host the control) with your VB program (or even the whole server - they can run anything you allow there) as if logged on at the server machine's console.
Of course now you need a REALLY BIG server because it has to be able to run maybe 100 copies (or however many users you have) of your VB application at the same time. This is NOT a scalable solution and isn't really putting your application "on the web" (ok, I've beat it to death now, I know).
Good luck deciding.
Remember, option (2.) lets you present VB forms to the user in their browser (if it can do ActiveX controls, basically IE only). The downside is you need to learn more about DHTML to make it work than option (1.) because you have to deal with <OBJECT> tags and most likely a lot of script.
If you want VB forms at the client I think you might want to look into "web classes" - though I suspect VB.Net has replaced these entirely with the "web forms" concept.