You can use the following code to store data in the module settings tabel:
Dim objMC As New Entities.Modules.ModuleController
objMC.UpdateTabModuleSetting(TabModuleId, "YOUR_KEY_NAME_GOES_HERE", YOUR_VALUE_AS_STRING_GOES_HERE)
To get the data back you can use:
Settings("YOUR_KEY_NAME_GOES_HERE"))
This works in a module code behind, not in you app_code. You'll need to get the module settings from the controller in the app code if that's where you need the data.
Be sure to check for null values and empty strings, as the settings won't be set until you have saved something for the first time.
DotNetNuke has a provided this very cool method for setting storage. There is a table called TabModuleSettings that stores key/value pairs like above. You can store just about anything there using the above code, but the value is limited to around 2000 characters. Mind you this is not the best place to store tons of data, because the values aren't indexed and you will fill up the table which every module on every page must use. Hoever, it is a convenient place to store data with out creating any kind of data provider.
You can check out the module template for Visual Studio and itwill have a settings control where you can see how it is typically done. Another option is to look at http://www.snowcovered.com/Snowcovered2/Default.aspx?tabid=242&PackageID=7332 which is a free module I wrote that has the source and models the save/get features.