Just a bit of clarification, as there are so many ways to pickle tomatoes and given how tricky pickling can be, I'd hate for anyone to start something likely to fail.
teatpuller's method is correct for r
efrigerator/quick pickles. These need to be refrigerated once the jars have cooled down. If you want crispy tomatoes, I'd recommend against cooking the tomatoes. Instead, as teatpuller describes, place the tomatoes in jars and cover with the hot brine.
You also can pour cold brine over green tomatoes and then
ferment them. Once fermentation is done to your liking, you can refrigerate them or can them (I haven't tried the latter). You want to use cold brine for this method as apparently boiling the brine may eliminate/reduce some of the good stuff you need for fermentation. I'm currently trying this for the second time. I tried this a few years ago and the tomatoes weren't good. We had sufficient green tomatoes this year that I thought I'd try it again. Fermentation is occurring, but I'm having to skim a thicker mold off the top of the crock that I usually have to with my cucumber pickles.
You can also
can green tomatoes. I recently canned some using low temperature pasteurization and a bit of calcium chloride. I'm hoping that the low temp technique and the calcium chloride will mean that the tomatoes stay crisp. I'm waiting a few months before sampling, so no successes to report just yet. I made seven quarts of these, so fingers are crossed!
And, one last note - - brines are generally different depending on how the tomatoes will be stored. You can't necessarily use a refrigerator pickle brine for a canned pickle brine. For example, for canned green tomatoes, I'd want at least 50% vinegar (at 5% acidity). With refrigerator green tomatoes, you can go much lower. And, fermented green tomatoes generally are vinegar-free - - there the concern is instead amount of salt.
Ronna