Well, without a lot more detail I can't guarantee that this will work, but you can normally ODBC to MySQL (preferably MySQL Server) and then back into a more common (Access, Approach, Alpha Five) format. In fact, all three programs can import from DBF tables, but Delphi sometimes presents certain challenges in getting an accurate and complete transfer from source to destination. You sometimes have to obtain an independent driver to allow your application to hook into the Delphi DBF files, since most databases assume that you will only ever want an MS DBF driver which sometimes is not sufficient to cut the mustard.
An excellent third party product you could consider is the DBF viewer available from the following link:
It's a cross platform multi-format product that can read almost all DBF files from just about every program that can make them.
If you can still work on a PC with Delphi you can export to a more suitable format (.txt or .csv are easy options but others are available) which could help get you up and running. The problem here is not that the files are DBF but that they are Delphi originated.
If this is not enough to get you going, post again with as much information as possible.