This is the pump with connectors for the 18mm hoses.
This is one of the hoses, I use this one to connect the tank to the pump. Because it's rippled it's a bit more modified than a normal 18mm garden hose.
It attaches to the bottom bit of the pump. I use another 18mm hose to attach to the top bit, and that hose goes from the pump out onto the lawn.
I start with the big tank, which has a separate plumbed connector for attaching hoses. The main reason is so I don't have to prime the pump, gravity does this for me.
Once I am finished draining the main tank, I use the valve on the hose to shut it off. I then disconnect it from the tank bit and attach it to the bit below, which just hangs over the tank wall of all the smaller tanks.
I open the valve again and the pump kicks in. The white valve you see below is redundant, I don't use that one at all. I just haven't taken it off the attachment
I hope that makes it a bit clearer of how things work.