There are two general approaches for integrating an ASP.NET app with Salesforce.
- Create a Canvas App in Salesforce that will surface your ASP.NET site in an iframe. Salesforce will POST a signed request to your ASP.NET site that you can use to verify the request came from Salesforce and get a valid Session ID for making calls back into Salesforce via the API.
- Create a Composite App. This is the older version of a Canvas App. Again, your ASP.NET site will appear in an iframe. Here the Salesforce SessionId and orginating Server URL are passed on the query string.
I'd say go with the Canvas App. You can easily play this within a Visualforce page as required.
Incidentally, there is a dedicated StackExchange site for Salesforce questions at salesforce.stackexchange.com.