I have one of those little Kenmores, a 158.1050. Yours looks to be a 1030 or 1040. I used to have a 1040 but I sold it to my former surpervisor for her daughter to use for 4-H sewing - went to a good home. They are a great machine. I have a full-sized Kenmore of the same age I got for my HS graduation gift, I wish they had bought me one of these cute little ones instead!
I have a .pdf manual I could send you if you did not get one with the machine.