mfds
I would second slim_slag's advice to read the AIM, but for airspace a brief summary is as follows.
By default:
Above 18,000 ft msl is class A
Between 1,200 ft agl and 18,000 ft msl is class E (over most of the continental US)
Below 1,200 ft agl is class G
By notification:
Major airports have class B airspace surrounding them, typically up to 10,000 ft, with base rising with radius.
Middle size airports have class C airspace surrounding them up to 4000 ft aal, with base rising with radius.
Almost all towered airports without B/C have a 5 nm ring of class D up to 2,500 ft aal.
In addition, most airports with IAPs have an area of lower class E down to 700 ft agl protecting the approaches, and some of those without a tower have a class E surface area around them.
The vis/cloud minima are similar to ICAO but in ft and statute miles. A significant difference is that the cloud clearance minimum at lower level is 500 ft below cloud or 1000 ft above. So you can't sneak into a control zone VFR just below the base as you can in the UK. Most VFR flying is done in class E controlled airspace, where no clearance is required.
Class C and D airspace require no clearance per se, but they do require two-way comms with the controlling unit.
Licence privileges are much simpler than the UK. IFR requires an IR. PPLs without an IR are restricted to VFR.