A good way to win your first few defenses is to place your cannon in the center of your base, then surround it with other buildings. Since most early opponents will bring Barbarians and Archers along, your cannon will be able to take them out easily while they are going through the various buildings.
On the attack side, most early opponents place their cannon behind a corner of walls, so using 4 cloaked Archers can take the cannon out from beyond the wall. Speaking of cloaked Archers, upgrade your barracks, troops, and army camps first so you can access cloaked archers and the new, stronger troop types. Don't upgrade all 3 defenses at first; focusing on building your army camps and upgrading your troops before upgrading all 3 defenses will have you matched against opponents who also got only 1 or 2 defenses, and those are easier targets for your stronger troops. Check out the whole guide for a few more tips.
Builder Bases don't have spells but, instead, have troops with special abilities. Upgrading troops unlocks their Special Ability, with each level upgrade providing increased benefits to a specific area. Once you get the Master Builder Hero, he can visit your home village and gear up defenses, turning one cannon into a double cannon. The Master Builder's Battle Machine (unlocked at Builder Hall 5) has a rechargeable ability, so make sure you keep an eye on its timer and use it as often as you canhe new Defense units are the Double Cannon, which unloads multiple shots but at a shorter range than your regular Cannon, the Archer Tower, which can be made to either shoot fast but at a shorter range or slow but at a longer range, the Firecracker, which is like an Air Defense but not as powerful, the Air Bombs, which provide a steady stream of air traps, and the Mine and Mega Mine, which can be switched to either shoot at ground or air targets. There's also the Crusher, which does huge splash damage but takes a while to reload, the Multi Mortar, whose long range allow it to take out ground units quickly, the Push Trap, which flings troops at a specific direction and can be combined with a regular spring trap for extra laughs, and the Guard Post, which is similar to Clan Castle troops.
In terms of strategy, Chief JuDoSloTh89 points out that it's still early to figure out the strongest tactics, but there are some general ones that have been successful so far. You'll want to get your second army camp up as soon as possible. In terms of troops, a small kill-squad is usually more than sufficient to take out key objectives in enemy bases. Early on, Mass Archers are very efficient. Baby Dragons are great in the Builder Base because they can take out targeting defenses quite effectively.
These are just early guides and tips, so keep in mind that they will change as players discover more things about the new update and figure out how to best use the new troops and new buildings. I hope you're enjoying the new update and your new base, and do let me know in the comments if you're happy with Supercell's direction with Clash of Clans.