First, buy two gnomes and position them as close as possible to the entry of where the bugs come in. Upgrade them both to level 1 rocket gnomes as soon as you can. Stop the upgrades at level 1 rocket for now. Purchase a Flamingo and upgrade it to a level 1 Super Flamingo. Stop upgrading it for now. Position it as close to the entry as possible. Purchase a Cherub and upgrade it to a level 1 Cupid. Position it as close to the entry as possible, thenfully upgrade the Super Flamingo and Cupid. Finish upgrading the gnomes. Positioning them close to the entry point will kill nearly everything immediately. If something gets past, you will have time to reposition your pieces. Remember to reset the pieces to the entry point before the next round. Watch the wave warning indicator to maximize damage to either the flying or land insects immediately at the start. This will often require swapping the Cupid and Flamingo around.
You cannot pass some levels without the assistance of Charlotte's Bug Houses. You can tell if you need the bug houses if your gadgets and plants cannot keep up with how many and how fast the bugs are coming. You need the bug houses to stop their progress so that you will have time to reposition your gadgets and kill them. Upgrade the houses so you can have several defensive bugs out at one time.
Upgrade your gadgets first since they are moveable. Get the Super Gnome as fast as you can. This rocket-launching gnomes carry a punch. Get the Super Flamingo next so that you can take out flying creatures. Once you have a few gadgets upgraded, get the Quick Deploy. You will now be pretty much unstoppable. After you improving all your gadgets, move on to improving plants and bugs.