Exporting definitely is a bad idea. If you export to, say, a spreadsheet, each of those 10 locations will have its own copy, and you won't be able to synchronise those ever again. The idea of a database only works when everybody uses the same data stored in the same location.
The two options you have:
1. Login to a server from that 10 locations using a VPN-connection.
2. Deploy a full-scale company network, so that central location can be accessed via that network.
I've seen both methods working in the company I work for.
MS Access really isn't a tool for sharing data other than the above 2 ways. You won't like at all what you read about that in http://office.microsoft.com/en-us/access-help/what-happened-to-data-access-pages-HA010030832.aspx
The usual alternative is to make the application web-based. A low-cost solution is programming it in PHP and using a MySQL database. Microsoft prefers that you you use .Net and SQL Server, but PHP/MySQL is good enough.
But, sorry, this involves code writing. Luckily, you'll be able to find tools (shareware or open source) that can generate basic applications from only the data definition. I don't have any experience with those, alas.
I have an MS Access database with some 4,000 records. I'm looking for the easiest way to export the database so 10 users in different locations can make use of it, both searching for records and inputting new records. It's a small company with limited resources and we're looking for a solution with no code-writing and a resonable cost. Any ideas?