OK get underneath the table because the rails are attached to the slates with large lag bolts. You will need to remove them first to get the rails removed. Socket wrenches can be used if your hardware allows it. You might be able to remove the rails with pockets and side skirts as all one unit. If not look inside the pockets for there attachment points to the rails. Again they will be attached to the rails either with large bolts or wood screws.
The important thing in all of this is to bag each item and clearly label on the bag what they were for. As you remove the rail you will want to mark the underside so that when you put the table back together you can assemble the rails in their proper relationship to each other.
After the rails are removed, you will need to remove the cloth. If there is a wood backer underneath the slates the cloth may be stapled to the wood use a staple remover (the upholstery type to remove. If there is no wood backer the cloth was affixed with spray adhesive. If that is the case the cloth can be removed by pulling it off the slates since it should have only be glued at the edges.
After the cloth is removed you should see some large screw heads that were originally underneath the rails. These screw connect the slates to the frame. Remove the screws and bag them.
When you remove the slates this is a two person job. You want to be very careful when removing them because they are fragile if dropped! Remove the two outside slates first, then remove the slate in the middle last, just to be sure that the weight is removed evenly, and the table does not tip. Remember these slates can be near 200 pounds each.
If you are putting the table in storage for any length of time I would suggest that you crate the slates. I have seen people use wooden pallets for a crate. You want something to put the slates in to protect them and to keep them from moving around or hitting each other while they are being transported.
After the slates are removed it is a straight forward job to disassemble the frame and legs. It should be very clear where the bolts and screws are when you are looking at this without the slates on top.
Take your time, mark all of your parts to make it EZ to reassemble, Bag all of your hardware and lable so that you know what they are and you don't use them. Above all be careful with the slates.