You don't sift it, you soak it. Take a bucket or container of some sort and put a load of clay in it straight from the ground. Add loads of water, take off your shoes and squidge the clay until it becomes a soggy wet runny mass. Leave it alone to settle and the impurities will settle to the bottom. The clay particles will also settle somewhere in the middle and water will be on the top. After a day or so, ladle the water out until you get to a thicker clay soup. Scoop the soup out until you get to sediment. Dump the sediment. It has all the impurities in it.
Take a large piece of cotton or linen sheeting (an old bed sheet will do) and pile the soup in the middle. Fold the sides in and start squeezing by rotating the ends in opposite directions. This will force excess water out while leaving pure clay inside. Once the clay is firm enough to hold it's own shape (it'll still be wet though), you can work it by hand to push more water out. Keep going until you end up with pottery quality clay. Put it in a plastic bag until needed. If it dries out into a hard lump, add water to reconstitute it.
To make primitive pots, take some of your clay, mix a little crushed eggshell or chopped straw in with the clay, even a little silver sand and make your pot.
Dry the pot slowly in the sun or by the stove but don't let it dry too quickly or it will crack. If it does crack, stick it in a box with all the other failures and reconstitute at a later date.
When the pot is good and dry, dig a trench about five feet long by two feet wide and about six inches deep. Light a fire at each end. Place your pot(s) in the centre and allow the fire to heat them up. When they are good and hot (too hot to touch by hand), move the fire inward bit by bit, keeping it fed all the time until the pots are covered by burning wood.
Build a pyramid of wood over the fire so you end up with a decent bonfire, but not extending the edge of the trench. Allow the pyramid to collapse in on itself. The heat generated in the middle, where the pots are should be enough to fire the pots. Keep the fire blazing for a few hours then alow it to go out by itself and don't touch until the next morning.
Carefully remove the ashes and you should have fired pots. The colours can be anything from red with black bits or grey with black bits depending on the type of clay you use. The black firing comes from the fact that the firing is uneven in this type of kiln fire so results can be unexpected.
When the pots are cool enough to handle, dunk them in a bucket of water and scrub them with a toothbrush to remove all traces of ash. If the pots soften and fall apart, they were not sufficiently fired. If the hold up, they are good to use to cook in/drink from.
If you make a decent size pot you can boil water, make stews, fry chips in it over the campfire. It doesn't have to be glazed.
You may find you have some pots that have broken in the fire (when wood collapsed on them). Keep these till next time and use them to cover your new pots as it will protect them.
Hope this helps, have fun.
Eric