I recommend looking at the shortcodes reference under the EVE ShipInfo menu in your blog: there are a number of examples there, ready to copy+paste into your posts. Beyond that, what you use the plugin for is left to your own imagination. The list and galleries shortcode offer so many customization possibilities that you will certainly find some creative uses for them.
Assuming you have installed the plugin, here are a few things you can try out to see what the plugin has to offer.
Showing an info popup when you click a ship name
Discover the almighty [shipinfo]Abaddon[/shipinfo]!
Doing the same with a custom link label
Discover [shipinfo name="Abaddon"]the almighty Abaddon[/shipinfo]!
Linking to the virtual page instead of the popup
Showing a list of all minmatar ships
Showing the fitting slots layout for all caldari frigates
[shipinfo_list races="caldari" groups="frigate" columns="name, highslots, medslots, lowslots"]
Selecting all ships with exactly 6 low slots
[shipinfo_list lowslots="6" columns="name, lowslots, group" order_by="lowslots" order_dir="desc"]
Selecting all ships with more than 6 med slots
[shipinfo_list medslots="bigger than 6" columns="name, medslots, group" order_by="medslots" order_dir="desc"]
Showing a gallery of all blockade runners
[shipinfo_gallery groups="blockade runner" columns="2"]