Moved from my fansite.
Study! : Check all your available prey. Study their defenses and plan the best strategy to get in and handle your business. As of right now the only reason to attack someone else is to steal resources, or for the simple pleasure of it.
Scout! : Your first wave of monsters should be scouts and/or tower attackers. I always start with around 40-50 Octo-ooze and fill in the rest with Pokey's. Find the general area you plan on attacking and send in 5 Octo's at a time. This enables you to locate Booby Traps without losing your entire army. Once your scouting is done, send in your Octo's in waves of 20 against Snipes and 30 against Splash. Once your Octo's are attacking the towers send in the Pokey's to assist them in finishing off the towers. Be careful as the Pokey's will generally target close by resources. The object of your first attack isn't really to do a lot of damage but to open the way for your next attack. If you get lucky or if the enemy didn't upgrade enough you will take out 2-3 towers your first run.
Attack! : Your second attack should be formulated to take out remaining towers or at least most of them. You should have your Locker at level 2. Some people have a difference in opinion of which monsters to use but my strategy has failed VERY few times. I recommend starting out by unlocking Bandito. So, build about 10 Bandito and fill the rest of your space with Octo's. Send in your Octo's in 2 groups to the location(s) your started on before. Let these bad boys get in and once they START attacking the towers send in the Banditos in 2 groups as well. 5 and 5. The Banditos will pull up, finish off the towers being attacked very quickly and the groups will spread out and attack other towers. If you are unable to take out most of the towers, repeat this step.
Pillage! : The last phase is the looting phase. For this I recommend 10 Octo's for each remaining tower and the rest Bolt's. If you were successful there are no more towers or only 1 or 2 left. Send in the Octo's at the remaining towers and toss your Bolt's away from the remaining towers but also away from any non-resource building. Preferably close to the Town Hall or Silo's. Bolt's steal more resources per damage than the rest of the Lv1 and Lv2 Locker monsters. You get resources every second on the countdown timer while attacking something with resources and 90% of the time you get a huge bonus in resources when a resource building is destroyed.
You can swap in and out whatever monster you wish but the general idea remains the same. Scout, Attack and then Plunder. One thing to keep in to consideration also is if you take out all their towers and you DON'T have any 'looting' monsters - end your turn. Even if you still have 20+ monsters. You want your 'looting' monsters to attack the Factories and Silos as they get more resources per hit than all other monsters.
*added*
When flinging monsters in, take in to consideration where towers are located at and how they will effect the outcome of the battle. You don't want to send in a group of 40 Octo's directly to a Splash tower. You want minimal damage. done to your own monsters.
Send monsters in waves to attack Splash towers. Send in your tanks first, then your damage dealers.
Image: Drop your tanks (high HP monsters) at drop zone 1. Once the monsters begin to engage the tower, drop in your damage dealers at drop zone 2.
Image: Same thing as the Splash tower.
Image: Attacking multiple towers. Send in your highest HP monsters to Drop Zone 1 to take on fire from the Snipe. Send in high HP monsters to Drop Zone 2 to attack the Splash from the bottom to draw fire. Damage monsters then get flung in to Drop Zone 3 to attack the Snipe without being in range of the Splash. Drop Zone 4 is for your monsters to deal damage to the Splash without getting hit from the monsters you flung in to Drop Zone 2.