This guide lets you quickly glance at the emblems to match up the best ones for the job during card battles. A blank section just means that element does not have a strength or weakness for that section, at least not listed on the in-game chart.

Adding the text here in case someone needs to copy/paste translate it.

How to read the Elemental Cards.
-Fire cards do only half the damage to Water and Ground cards.
-Fire cards do double the damage to Grass, Ice and Animal cards.
-Fire cards take only half the damage from Grass, Ice and Animal cards.
-Fire cards take double the damage from Water and Ground cards.

These are the abilities listed on the cards for the turn-based tables. If you click on them in your collection book you'll see the ability on the right-hand side. There are spelling errors and they sound a bit broken in translation but I'm just putting it as-is from the in-game text.

From what I can see all cards have the normal elemental ability but cards with the "EX" in their name have higher values in their ability and some have bonus abilities, except Fire for some reason unless it's a misprint. Also, Ground just says "Fight back" I don't know if that means they counter or what. I've not played the turn-based tables myself yet but I'll update this after I do.