or if necessary cutting the side frame brackets...(by the way be sure you have electrically disconnected first (after first having shut off power at the panel - either circut breaker off or fuse removed) check your owner's manual regarding precautions in the electrical area (like pre-discharging capacitors, etc.), then remove the lower access panel (or so-called kick-plate), then disconnecting the water supply.... next disconnect the under the counter support bracket screws.
get yourself two 2-4" wide, 1/4-1/2" thick 23" long strips of wood and a 2'x3' sheet of masonite, thick appliance box cardboard, piece of used carpet(upside down) or plywood. Cut each strip of wood to shorten so that you have one that is about 18" long and the other is say 5" or so long.
Next get yourself a wedge tool, like a crow-bar or something...slip one of the longer slats of wood down the inside towards the back wall, wedge up the back frame support or leveling leg and slip sideways underneath the long slat of wood...
do the same on the other side
Now returning to the first side, do the same and sideways slip the short slat under the front foot, in front of the longer slat that is back towards the wall.
Put your floor protector (plywood, upsidedown carpet, cardboard, etc.) in front of the DW..
slowly using your wedge tool..."encourage" the DW up and down, back and forth to walk forward onto your floor protector (sometimes lifting from inside the diswasher with the door open or against the sides to lift it slightly...get it closer to your floor edge.
Sometimes you need to take a hacksaw or recip saw and cut away at the frame supports.
Oh....remember your drain line...you'll need to disconnect it and thread it back through your cabinets into the DW compartment space to pull it through.
You can also (since you are replacing DW so it won't matter to you) with the DW door open...pull and lift and wiggle left and right as you draw it forward and up onto the floor protector the DW using the door
Another, if available, useful tool are those hard plastic carpet/floor protectors that are used in carpeted offices underneath office chairs with casters - if you slice those down to strips - they work well (use upside down if they have teeth on the carpet side) and as they are flexible you can slide a strip under each side leaving the end long out in the room and just pull on the strips to pull the DW up and onto the floor.
Once you get the face of the DW out beyond the counter, the rest will be really easy as the top height of the rest of the DW is usually much shorter than the frame...its that first inch or few that is the toughest (the rest of the frame also is usually skinnier by at least a 1/2" past the face frame.