Cobbing by hand is more gentle and controlled, creating more finished walls. Hand cobbing will allow you to build up a little further before the cob starts ooging because your weight is not added to the wall.
To loosen the cob from the tarp and make it easy to pick up, roll the mix in the tarp like you would for stirring. Lift handfuls of cob onto the walls and massage it all together with your hands and a stick.
Thumbs are a great tool for the job but they do get tired, and thumb nails get sanded-down from shoving them into the cob. Give your thumbs a rest by replacing them with a stone or stick part of the time. You can use your palms and knuckles too. One hand can be the form as the other compresses the cob against the form and incorporates it into the cob below it.
It's easiest if you can keep your upper body weight over your arms, using gravity to help you push and massage the cob together.
It's important to make your house one massive hunk of cob, avoiding weak connections between 'layers'. When adding cob to a wall, you may need to re-wet the last application of cob so it's soft enough to massage the new cob into it.
Do not smooth out the surface of the cob too much or it will dry as a hard skin, which will slow the drying in the wall beneath it.
When you're cobbing, you are creating a surface for future cob to be built onto. Make sure you get into the habit of making a flat surface on the top edges of the wall, not a rounded one, so the next "layer" of cob has ample surface area to sit on comfortably, instead of sliding off.