The Sylvan starter deck army is Roots Have Arisen.
Stated often as the "beginner" domain, Sylvan is a domain that's main focus is rush: spawning weenies and overwhelming the opponent by sheer numbers. However, there are other strategies that can be utilized to take advantage of the Elves and their Treant friends.
Many "Tree" decks are based of the Treant's ability to spawn from forests, allowing creatures to pop out of nowhere since Treant's become Seedlings upon death and spawn in Forest.
Another clever strategy to take advantage of is Sylvan's powerful range: Alearwyn Barque can become a mobile turret provided their is enough water, and The Coldstream Guards and Tenderfoot Archers are a good response to cards that are dangerous if attacked close range like Leprous Shambles. Spaf's Greatbow is especially good proof of this, but keep in mind that you must see the enemies before you can rain arrows on them.
Sylvan also has some good "flying" creatures: Thistle Falcon makes an excellent earlier game harasser, Goose Tamer is a ground creature that "breaks the rules" and bypasses terrain easily, and Barkskin Dragon and Pixie Queen are at the top with powerhouse and stopping creatures dead in their tracks respectively. Keep in mind that Pixie Queen cannot enter water though and Goose Tamer still takes damage if it ends its turn in water.
Ascent is a good way to get rid of opponent's creatures and Entangle can serve a similar purpose as long as your opponent doesn't run Ocean or Desert-based decks. Mis-Scribed Circle is a "Swiss Knife" that has many uses: protecting your creatures, damaging opponent's and aggressively exploring the map. Teleport is the best of the four against creatures, dealing an easy 2 damage by sending a creature to water or relocating a it to a different area.
Other useful cards are Loyal Wilds, a way to disrupt control, Restore Nature's Balance, a useful disenchant, Beacon of Celador, a building that can shift Sylvan units around the board, Ivory Spire, a Building that has a huge vision, Treetop Dominion, a powerful source of domain, and Bamboo Watch Tower, providing 2 vision for a cheap 3 flux.
Overall, Sylvan is very speed oriented and a good player should take advantage of this. Bamboo Watch Tower can be used to grab your other flux well quickly, while you rush weenies and buildings toward the center well to try and protect it from your opponent. Once you've gotten enough domain, bring the Big Guns out in form of Spaf's Greatbow, Pixie Queen, Loyal Wilds, and other cards to make a formidable late-game offensive.
Domain isn't really a problem to Sylvan as they have many weenies and an easy way of getting domain through forest, which works well with their Treants. Plan on using cards that can cancel out enchants like Disenchant and cards that change the terrain like Cartographic Error. Creature wise, try to bring out stronger creatures that can withstand their range and quick ones that can stop weenies from randomly showing up in spots you weren't thinking about. Maintaining defensive range isn't a bad choice either: Sylvan has some good access to flying creatures.