hi, I was wondering how the leaderboards work and how you can participate in them. Can you help me?

Are you referring to the weekly/overall charts?

Getting into the top 10 slots of the weekly charts gives you 10 gold for each time you place, which is quite nice! Unfortuantely, it's rather hard to do so.

Weekly battle = number of victories of each pet that has participated in the Arena this week. This is probably the easiest way to get into the top ranks, as it requires just one pet with very good stats. (I've had the best luck with Lykos that have Tireless Heart, since the 5 extra energy points mean they can fight more often than other pets.)

Weekly breeding trade = number of times each user's pets that are up for breeding trade have bred. 

Weekly pet trade = amount of silver earned by each user from pet trades. 

Weekly item trade = amount of silver earned by each user from item trades. 

As far as I know, the overall charts don't confer any benefits (beyond bragging rights, I suppose!) They cover all of the areas that the weekly charts do, plus Battlefield victories. 

So the weekly battle means one pet needs to place, it doesn't sum up all of a user's pets' successes?

And weekly breeding trade DOES sum up all of the breedings from one user's pets? 

Thanks!

Yeah, that's correct!