I have some vague knowledge about the philosophy that schemes should be thought of as similar to topologic spaces, and we should divide everything by homotopy, and that the space should be actually sheaf in a correct topology.

Could somebody provide a concise and modern introduction that would allow me to work with statements like (from an answer to question about motivic cohomology)

K(Z(0),0) is simply the constant sheaf Z.

(+I wonder what the tag for the homotopic theory of schemes should be?)