The traditional method of stratification is to seal the seed in a bag with moist seed compost or perlite and leave in the 'fridge for a period of time.
The problem with this is in seeing when germination has started as this requires the bag to be opened, the mixture stired around whilst looking for the seeds, etc.
I prefer to use the method described by Dr. McAllister which uses a petri dish with moist filter paper.
For those of us without access to filter papers, (though these and petri dishes can be bought on eBay), a pad of kitchen tissue can be used, although it is best to avoid any with printing as the inks may inhibit germination or possibly poison the seed if copper based pigments were used. If you can't get petri dishes, any small plastic container will do, although these will take up more room in the 'fridge.
The dish can be easily checked for signs of germination and any such seeds removed and potted up. The only problem with this method is, if the root has developed, the root hairs may have penetrated the tissue and care is needed to remove the seed without damaging these hairs. I cut away a section of the paper around any root with a scalpel to avoid this damage and seeds planted up with pieces of tissue seem to grow on OK.
Academic citations quote specific temperature ranges and times for stratification which cannot be duplicated with a domestic refrigerator.
The system I use is to place the seed in the 'fridge for about a month, removing any which germinate, and then take the dish out of the 'fridge and leave it at room temperature for another month. If there are still ungerminated seeds left at this time, the dish is returned to the fridge for a second month of cold treatment. I often find that there is a burst of germination when a dish is first removed from the 'fridge.
I'm trying a different method this year as I've had difficulty in moving germinated seeds as the root hairs penetrate the tissue. What I've done in the past is to cut away a piece of the tissue as described above, but some seedlings transplanted in this way have died.
What I'm doing is to plant the seed in small pots, (5 or 8cm square), cover with Vermiculite and then a piece of heavy fleece to keep out the mice. Any pots that I feel are in need of stratification are then placed in the fridge in a poly. bag.
I'm now using damp compost in the petri dishes which should avoid damage to the root hairs when potting up. This takes up far less 'fridge space than pots of compost.