Peel and cut potatoes into medium size pieces. Slice the celery stalks and chop the onion. Add all this to a large pot, and add water just to cover the vegetables. Cook this until barely tender when pierced with a fork. I usually add a good amount of salt and pepper to this and if celery has leaves, cut up these and put in also.
While vegetables are cooking, I cook bacon, either in microwave (to save the mess)! or on stove, till just barely crisp. Drain on paper towel the break into bite size pieces.
When the pot of veggies is done, DO NOT DRAIN, just mash with a potato masher to get large chunks. Now add the clams and all the juice,the bacon and the milk. Take off heat and stir. Now just add the saltine crumbs to thicken. Add a little at a time, soup will thicken really quick. Now taste it. Add the salt and pepper to your liking, put back on heat and simmer for about 10 minutes. Depending on how thick you like your soup, you can always add more crackers.