You use css the same way as you would in html.
More specifically, make a tiddler with whatever name you want and put this css in it:
.alternating-rows tr:nth-child(even) {background-color:white}
.alternating-rows tr:nth-child(odd) {background-color:lightgrey}
give the tiddler the tag $:/tags/Stylesheet and save the tiddler
then using what you have in your post just change the first line to
<table class=alternating-rows>
and it should give the table alternating background colors. You can change the background color or add whatever css properties to the even and odd rows independently by editing the css.