extending my network with a switch

1) Technicallay can I do this

Yes

2) What is the actual product I need, I think a Switch, but reallly have no idea?

You need an unmanaged Gigabit Ethernet switch. Switches come in 5-port, 8-port, 16-port, etc versions, so you would want to buy a switch that has at least a few more Ethernet ports than you think you might need at this point, since the ports usually fill up faster than expected.

For example, if you chose a 5-port switch, 1 port will be used to connect the switch back to the AirPort Extreme, so you will have 4 available Ethernet ports for devices. With 3 devices connecting, that will leave 1 port open for future expansion. For just a bit more money, you might consider an 8-port switch if you think that your network will be expanding in the future.

Any computer / electronics store will have a selection of switches from which to choose. Personally, I have always used switches from Netgear, but there are any number of good choices as well.

Also, I assume a switch needs a power source?

Any Ethernet switch will come with an outboard power supply, which will need power from an AC wall jack.

3) Will there be any significant drop in internet speed for the items receiving signal from the switch.

No, assuming that the Ethernet cabling and Ethernet connections are all working correctly.