Are you sure you have a cable?? If indeed you do, you'll have to remove the instrument cluster bezel trim piece, ( it only has 2 screws) then remove the 4 screws holding in the speedometer cluster. Once you've done this, pull the cluster forward and you should be able to reach behind it and tighten the cable. You'll also want to check the connection on your transmission. I really don't think you have a cable. My 93 doesn't, the speedometer is controlled by the vehicle speed sensor on the tranny.
A '93 Geo Prizm is a SECOND generation vehicle. A FIRST generation vehicle (like my '92 Geo Prizm Sedan) is anything prior to '93 (for the Geo Prizms only). My Geo DOES have a cable. There are minute differences between the generations (there's three of them), so look them up in either a Chilton's or Haynes' Repair Manual for a better diagram to compare the differences. Wikipedia also lists the different generations, engine types, etc. for Geo Prizms including years, LSI/GSI, etc.
Are you sure it even has a cable? If it does, you need to remove the instrument cluster and disconnet the cable from the speedometer head. You should then be able to just pull the cable out. If it's broken off, you'll have to remove the cable housing from the transmission and just replace the entire thing. My 93 Prizm doesn't have a cable, it's electronically controlled by a Vehicle Speed Sensor on the transmission.
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