Unfortunately, you didn't provide a lot of information in your post as to what the problems are.
As people have pointed out, there are a ton of USB to Serial solutions out there so having the modern hardware with the ability to communicate over RS-232 is generally not a problem (although, depending on the connections used, you might want to invest in a RS-232 breakout box and read up on RS-232 handshaking as many of the older devices do use hardware handshaking). I have a few hand wired 9 pin to 25 pin connectors with the CTS-RTS and DSR-DTR pins shorted together as they can simplify your life immeasurably.
In my experience, the biggest problem is retaining floppies & CDs with the original software on them (assuming that the developers are no longer supporting the product/are out of business). If the company is still in business, usually they're pretty good at providing updated software for their products. If they're not in business, then look to see if they were bought out by anybody. Chances are you'll find that the purchaser is still supporting the product, although it may be under another name.
Personally, the biggest issue that I see when I have encountered this type of situation is that the original programs are on floppies. If this is the case, you will need to find somebody with a Windows/95 machine that they're keeping together with spit, bailing wire, gaffer's tape and good intentions - you should be able to copy the program onto a USB key and then burn it on a CD/DVD for more permanent storage.
Once you have the program in a media that you can work with, you may have problems with the installation. You will probably have to create a virtual machine on your PC AND there may be 16 bit programs that you have to convert to 32 bit - here's a great resource that's saved me a couple of times: http://www.reactos.org/forum/viewtopic.php?f=22&t=10988
Finally, Google is your friend. Chances are the answers are out there for your particular equipment.