In texts about feudal and post-feudal europe who owns land is of major importance, and it is clear that land cannot just be owned by nobles and the church, but also by the king.
How does this work though? It is not possible for a single individual to administrate any significant geographical area on their own, so they need people collecting taxes and so on for them, but as I understood it this was the job of the nobility.
Does the king have non-nobles administration his crown land, and if so, how does he maintain their loyalty without making them nobles?
You've answered your own question as far as the nature of Crown Land goes - it was land that belonged to the monarch.
She or he would administer matters through their Privy Council although mundane questions would be unlikely to reach royal ears, they'd only be involved in hearing protests about who-owed-what-to-whom.
Nobles who owned land or who rented Crown Land would be allocated a tax-payable sum based on the size of their land and the nature of their business, and would also be expected to provide a certain number of soldiers (under the arms of the particular noble) when required to do so, these allocations were divided up into areas called wapentakes (or hundreds).
Nobles wouldn't get particularly involved in property matters either although, like the monarch, they would hear matters of dispute, and there are plenty of those in historic records.
The day-to-day tax collection would be undertaken by paid tax collectors, bailiffs and sheriffs who would be organised by the landowner's chancellor or "keeper of the purse".
Taxes wouldn't just be taken on the land but on the waters surrounding them and all activities. Crossing a river? Tax. Using a particular road or bridge? Tax. Building a new barn? Tax. Come into a lot of money from a good wool deal with Belgian monks? Big Tax. And that's before you've paid your tithes to your local Archbishopric. Death and taxes have been a certainty for a very long time.
In all the cascading system of tax management is one of the wonders of administrative history and it's one that we often credit to the Normans, in fact it goes back even further to rulers like Alfred and Aethelfled who, as the Normans did, understood the importance of getting as much money as possible in order to maintain military forces. And to buy nice clothes with golden sparklies.
Perhaps the greatest early record of the taxation system is the Domesday Book which carefully lists every known settlement, the number of occupants, the number of livestock and the amount of farmable land. This wasn't for the amazement of later scholars but for the specifically-recorded purpose of gauging taxation.
Sources:
Medieval English Peasants and Market Involvement, Biddick K, 1985
Landlords, Peasants and Politics in Medieval England, Aston T, 2006
From Domesday Book to Magna Carta, Poole A L, 1993
And, obviously,
The Domesday Book, Conqueror W T, 1066