Correct way to wire an Alpha TX433S/RX433S
You must connect all Gnd pads.

The Arduino has an SPI function you can use. You need to wire the SPI pads (SDI, SCK) to the Arduino SPI pins. You also need to connect nSEL to an Arduino output.

FSK is the data input.

You can ignore the interrupt output.

You need suitable antennae, a simple 1/4 wave piece of wire should work.

You have a lot of learning and experimentation ahead of you.