Uaually, an AT mobo has a big DIN keyboard connector mounted on the mobo, and that's it, whereas an ATX board will have the keyboard, mouse, parallel, serial and USB ports mounted on the mobo. Also, an AT mobo will have two blocks for power connectors, in a single line, whereas an ATX mobo will have a single block of two rows (note: some AT mobos accomodate both AT and ATX power connectors [eg. FIC VA-503+]).
An AT PSU has two connectors to the mobo, and one to the case switch. An ATX PSU has a single power connector to the mobo, and the case switch connects to the mobo also.
An AT case will have the case switch connecting directly to the PSU, whereas an ATX case will have a much smaller cable connecting to the mobo.