It is a pretty big job. Get a shop manual from auto zone or AUTOBOOKSONLINE.COM
This requires the removal of the: Glove box, stereo, heater controls(cables), gauge cluster, head light switch, ashtray.. and basically anything else needed to remove the dash. The Core is buried in the heater box that can only be accessed with the dash removed.Walkthrough With PicturesThe above states that basically the entire dash has to be removed to access the heater core. This is true of the second generation (new style) S-series vehicles, but not of your first generation (old style) vehicle.
See the Related Link for "Heater core replacement procedure." below for the walkthrough with pictures.
*Added Comment* The above statement is true. The older style does not require the whole dash to be removed. I have changed the heater core in my 1991 S10 Blazer and it is still quite a job. You have to remove the radio to access a couple screws to the heater core cover. Also if you open the glove box you will see an access cover that is secured with one screw. Take the screw out and pop the cover and you will have access to a couple more screws to the same cover. The rest of the screws can be accessed under the dash. Once the cover itself is removed you will have access to 4 screws that hold the two straps. Once those are removed you can remove the straps and the heater core. Make sure you have disconnected the rubber lines from the heater core first! These are under the hood right under the blower motor and beside the HVAC cabin. Reverse for installation. - jedgell233