How do I use a transistor to up the power of a PIR output?

Hi, I need help.

You see the street I live in has more cats than, well the musical cats,  and seeing as my garden seems to be they're preferred  choice for going to the toilet, I decided to build a motion sensing water sprayer.

So off to Amazon I went and purchased some PIR sensors, a solar pump with a DC connection, bread boards wires and batteries and chucked it all together. Now the sensor will light an LED no problem but when I switch in the pump I get nothing. I read on tinternet that transistors can be used to up the juice but I was already far beyond my knowledge of circuits, components and the like. I even tried looking at sketches of PIR sensors to transistors, but after weeks of trying I'm no closer and have nothing to show for it but a headache.
If anyone can help and describe to me (in child like, basic terminology) how I wire up a transistor to a PIR and then a 4-12v 3.5watt pump that would be just super.
Or at-least put me out of my misery and tell me it's not doable.