Create a web server that can manipulate your Access database, this is the basis. There is a recent thread where someone tried to do it but others are having problems with it. However, there are more options: you can easily create a web server with python, there are python libraries that can read/write to access tables. I would do it via NodeJS and the express library using the ado library from npm.
Once the server is ready, you have two options:
1. Create a responsive web application (responsive means it resizes according to the screen gracefully). This is cross platform because it only needs a browser. Any device with a web browser can use your app.
2. Create an android app and a iOS app.
In any of the two options, you will use the same web server. I recommend the web app, it's less problematic. But native apps have a ton of advantages, like dedicated storage and more solid UX.
Once you have everything ready, deploy the server and the app or apps. There are plenty of options for your deployment.