What I have done is take a saw and set the blade depth so it just cuts deep enough through the linoleum and underlayment. First put in an old blade that you dont care about. Cut in straight lines about 4″ to 6″ apart, dont worry about hittin nails or screws cause you just cant help it. Go slow with the saw, when you hit a screw or nail just move over a little bit and continue. I go with this route cause tryin to save the underlayment is not worth the time it takes to try to save it. After you have done all the cutting then take a flat bar hit it w/hammer to jam it under the underlayment and it should pry up w/out too much trouble even with the screws. After you have all the underlayment off then go back and use screwgun to pull out all the screws. If they covered screws with a floor patch, put ample pressure on screw head w/screwgun and it should come right out. Done this method many many times.