Ideally, you'll be able to trowel down each layer of the whole floor in one day. You can mix up enough material for the whole floor layer a day or two ahead of time and let it cure. For a big floor, start in the morning so you'll have the whole day to put it down if you need it.
Make sure the base for your cob floor is as clean as possible. The base then needs to be dampened. Otherwise, the dry material under the floor will suck the moisture out of the floor quickly, and it will be more likely to crack. Spray it lightly again and again so it soaks in well but doesn't create puddles.
Start laying the floor furthest from the door, working your way toward the door. That way you can get out without walking over your beautifully troweled floor. Oops!
Working back and forth across the floor, add a 1/2 to 1 inch layer of floor mixture in reachable swathes (2 feet or so). Leave the edge slanting toward you (45 degreesish) and scratched to make a rough surface for the next strip of fresh floor mixture to adhere to. Spray the slanting edge with water when you're ready to attach the next bit to it. Lay your next strip of floor, etc., etc., until you're done!
Around the edges, where the floor meets the foundation or the walls, is a tricky place. The already dry walls quickly sap the moisture from the floor where wall and floor touch.
Sometimes the floor will shrink away from the walls as it dries, leaving a gap there. You can take some of your floor mixture and let it dry a little, or mix in some dry ingredients until it's as dry as it can be and still be malleable. Squish this together in your hands, roll it into a sausage shape, and put it down around the edges of the floor. Trowel it flat as you do the rest of the floor. The drier mix will minimize the shrinkage. (Thanks Athena! Good idea!)
After the first layer of floor has hardened to the leather-hard stage, you can add the next layer. When your last layer of floor has hardened to the leather-hard stage, go back over it with a squirt bottle and trowel if you want a glossy smooth finish. Stand and work from plywood squares to minimize footprints.
If you've used too much clay and the top layer cracks, you can add another very thin layer of floor. Remember to dampen what's there before applying the next layer.
How to connect one day's floor work to the next
Sometimes it turns out that you can't do the floor in one fell swoop, or that you need to join the floor of a new addition to an old floor. Where the floors connect is a potential weak spot. If you know you'll be adding on to a floor, make sure you leave the edge sloped and scored well. That means scratch it up so the surface is rough and the next layer will be able to key into the scratches. When it's time to add on, wet the sloped edge really well and trowel down the new floor.
Save some of your original dry mix so you can use it for repairs later on.
The floor doesn't have to be exactly level. Slight undulations make a floor feel more natural and friendly. Have you ever seen anything (other than water) perfectly level in nature?
Establish where you want the floor height, and draw or snap chalk lines on the walls or foundation to guide you when you're troweling down the floor.
You can use a 2x4 with a level taped to it, and drag it across the wet floor to "scrape" it level. You can lay down guides running parallel to each other and close enough for the 2x4 leveler to span. These can be made of thin stops of the floor mixture or thin strips of wood that need to be removed as soon as possible and the gap they made filled and troweled.
Here's a little trick to prevent you from getting too far off level. While you are putting the base in and/or troweling the floor surface, nail big headed nails into the ground with the tops a tiny bit lower than the final floor height. Start with one nail and level the tops of the other nails to it and then to each other. Put them as far apart as your longest level will reach. This will give you a guide while you are putting down the floor. The last layer of floor can cover the tops of the nails. You could use little piles of the floor mix in place of the nails. Let these dry some before putting down the floor, so they're hard enough to hold up to the leveling job without squishing.