CRM provides a component called the Data Migration Manager, and it's this component you will most likely use to translate information from Access into CRM. The draw back is there is no direct database-to-database interface, and you are limited to exporting and importing your data in an intermediary CSV, flat-file format.
Another potential drawback, and it's perhaps the most annoying, is that the CSV format used for importing does not handle mixed value encapsulating formats that Access and Excel use for exporting. For example, Excel and Access will alternate encapsulating data with quotes depending on whether the value for a particular field includes a space or comma. The Data Migration Manager (DMM) does not like this, and will expect either all data to be encapsulated with quotes, or not.
Another formatting issue you may encounter is fields with multi-line values. The DMM expects all end-of-line codes to signify the end of one record, and the following line to be the start of another.
When I'm migrating data, I routinely run the CSV files that Excel or Access generate through a parser to clean up the formatting. An excellent tool for this is TextPipe Pro. Once you have your CSV files in a proper format, the DMM works perfectly.
It is NOT recommended or supported to make direct SQL calls (insert, update, etc.) on the SQL databases/tables that represent CRM, and in many cases this may corrupt your data--so aside from the DMM, the only other option you could have is a 3rd-party application or an in-house application to convert the data for you, and function as a database-to-database conversion.
As far as interfacing Access with CRM, this can be done with a simple ODBC connection directly to the SQL database, but you will be limited to using read-only views. I would highly recommend the "Working with Microsoft Dynamics CRM" books to understand the different record types and processes within CRM to understand how best to translate data from your existing database.
Deploying CRM is not a decision you should make lightly. I think it's the best product Microsoft has ever produced, but it's not without its own limitations, and may need significant customization for your business needs. Your best bet is to contact a CRM solution provider to examine your current databases and processes, so that an appropriate, professional determination can be made as to your particular upgrade path.