Ah, free-enchanting is a lovely art! If you're not a lucky sort to get a nice bundle of stones out of lucky capsules (or prefer to spend your cash on things like the Boss Vault), there are still plenty of ways to get your weapons up to snuff...
1.) Log in daily. The prizes increase until you're getting three or four stones a day just for popping in!
2.) Visiting Friends. Even if they haven't played in four months, keep around fifty friends and pick up enchant stones (along with 20 energy and 200 gold!) every day.
3.) Daily Victory Bonus. Your first battle won each day gives you three more stones!
4.) Sweep Chest. For winning all three battles on a single card, you get a chest full of gold and often one or two enchant stones.
5.) Daily Spin. You get a free one every 24 hours, and can win two enchant stones with a bit of luck.
Between all of these, it gets relatively easy to pick up the stones you need to attempt enchanting in higher levels. You can give an attempt every two or three days (depending on level). My only tip for the actual enchanting is to focus on one weapon alone at first, saving leftover stones for another attempt once you hoard enough.
I wish you the best of luck in your enchanting; you'll get it eventually!
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