Begin by washing and removing the cores from the tomatoes. Cut out and discard any bad spots. Quarter your tomatoes & squeeze out most of the seeds & juice. If you leave all the juice in - your sauce will be watery (thin). Use your hands to squish all the ‘maters into mush. Put in heavy bottomed pot & put on stove turned to medium heat.
Dice onions & mince garlic. Saute them in a hot skillet with the olive oil. Once onions are clear, add them, garlic & oil to the pot of tomatoes. Add salt. Bring it back to a simmer. Use an immersion wand to blend the contents into sauce.
Chop your fresh basil leaves & cram as much as you can possibly get into 1/2 Cup. You want lots of basil – it’s wonderful. Toss the chopped basil into the sauce & continue to simmer. The sauce will have a red-orange color with pieces of fresh basil floating around. Taste your sauce & add more salt if needed. Cook until desired thickness (if you removed most of the juice you won't have to cook too long).
Add 1 tablespoon bottled lemon juice to each pint jar. Ladle hot sauce into hot jars. Leave 1/2 inch headspace. Wipe rims clean and adjust 2 piece lids. Process in boiling water bath for 35 minutes. Begin timing when water boils.
For a step-by-step on hot water bath canning go here.
Disclaimer: Always follow directions specific to your equipment and elevation for canning. Dispose of any home canned goods that show signs of spoilage which can include: bulging lids, leaking, corrosion, cloudy, mushy, moldy foods or disagreeable odors.