I make lots and lots of wine, but don't have a press!
Just yesterday, I pulled the bag of fruit from 2 gallons of chokecherry wine. Bob sanitized his hands and arms and squeezed the bag of fruit until the juice stopped coming out. That's how we "hand press" ALL of our wines!
Typically, you ferment on the fruit for the first 5-7 days (depending on temperature) and pull the fruit and squeeze. We always freeze the fruit first, to make it more "mooshable" after it thaws and ferments. Using the canned stuff is fine, and using hot water (to dissolve the sugar) means that the fruit puree will be able to mix decently to give you a close OG. Use a big bag, so that the fruit is very loose (not packed in) and the liquid easily permeates it.
A typical schedule would be:
Mix up must:
big mesh bag with fruit
water and sugar (according to recipe)
Acid blend/tannin/etc (according to recipe)
1 crushed campden tablet per gallon (dissolved in some of the water)
Twelve hours later, add 1 teaspoon pectic enzyme per gallon
Twelve hours after that, add your yeast.
Ferment 5 days, until fermentation slows down. SG should be 1.020 or less. Squeeze fruit, and transfer to secondary. Don't transfer all the lees. Top up, if fermentation is slow enough (so you don't have a mess), or top up a couple of days later if fermentation is still vigorous, and airlock. Rack whenever lees are 1/4" thick after 45-60 days. Top off at each racking with similar wine, or water.
That's about it!