I need help. I've been trying since I joined yesterday to catch a Sylvestie and I still haven't caught a single one from a battle. The only one I caught was a weak one in one of the decision thingies. What am I doing wrong? I can't afford another trap. I've used the three from the fairy and another three or four I bought myself. I know sometimes they fail, but they have to work sometimes, right? What am I doing wrong?

Firstly, you need to ensure you're using the right kind of trap:

Green for common and uncommon sylesties
Blue for common, uncommon and rare sylesties
Purple for common, uncommon, rare and epic sylestis
Red for any and all including legendary / mythic

Common = no coloured stars
Uncommon = green coloured stars
Rare = blue coloured stars
Epic = purple coloured stars
Legendary = yellow/orange coloured stars
Mythic = red coloured stars

I find I burn through multiple traps unless I use a trap that's a least one trap above the minimum that would hypothetically be able to catch the sylesti. For example, if I were after a sylesti with blue stars (a rare sylesti so it should be catchable with a blue trap), I'd use a purple trap (and even then I typically go through about 2 on average).

I don't know if it helps but I also feel better if I reduce some of the sylesti's health in case weakening it might make the traps more likely to succeed. What you have to be careful of here though it if you've got any abilities that your sylesti may have which will cause damage across multiple rounds (e.g. slash) as you don't want ongoing damage to cause the pet to be defeated before you catch it.

I'm sure there's a Guide around somewhere but I can't find it right this moment. I'll have a look and re-post if I find it.

All that said, are you just looking for some new pets for your Stable? If so, you could consider buying a sylesti from another user as opposed to trying to trap one? You can search for relatively cheap sylesti as follows:
Click Advanced Search in the left hand column
Click Search Pets
Select Gender, Species, etc
Where it says "For Sale" change from "Any" to "Yes"
Where it says "Order By" change from "Pet ID" to "Sale Price"

Here is the Guide I mentioned :)

Thanks for the help. Unfortunately I can only buy the one type of net right now, so I guess it's probably best if I don't waste my money?

You could wait, certainly (I don't find trapping pets particularly cost effective at all, myself). I believe the next trap type is available once you reach Umbra Forest. I don't doubt that you'll have plenty of opportunities to catch nice sylesties in future - I see quite a lot of nice ones in the Nightfall Bandit Dungeon which is the last section in Viridian Meadows.

Just a thought though, if you go to the trader in the Festival zone (directly down from where you enter the Festival zone map), can you only buy the one colour trap or do you have three to choose from? Could be a workaround until you get to Umbra Forest?