Disconnect the negative cable from the battery, then there are three studs and one bolt holding the heater box which the heater core is in there are also a few vacume lines and the heater controls that are attached to the box lwhich must be removed. There are the heater water lines that need to be removed under the hood, the studs (3) have a nut that is accesable through the hood, the bolt is accesable through the inside on the passenger side firewall. you will need to remove the airducting that is under the radio top of the engine cover and remove the bolts that hold the dash in place.However it is better to unscrew the defroster ducting on the dash.
After you remove the box then you can access the core by removing aproximatly 6 or 8 screws that hold the rear cover of the box together then you will see the core which is held down by 2 hold down brackets.
Please check this links to get a detailed idea about how to replace heater core.http://www.ehow.com/how_5306495_change-heater-core-chevy-blazer.htmlhttp://www.superchevy.com/tech/sucp_0707_remove_and_replace_leaking_heater_core/viewall.html
However you did not mention the model no and the year of your vehicle.But this is the general way to fix the problem in heater core.
Hope it will help.Also you can get back to me if you need further assistance.