1. The Bathroom comes first.
You know that the bathroom is going to be the most work, so start there. It's the most important room in your apartment because it's where most people spend the greatest amount of time. Take everything out, the stuff on the sink, the bathmats, even the stuff in the shower, and give it a good scrub. If you can do that once a month, it'll make you feel all around cleaner. Don't forget to swifter the dusty areas on the floor, it's not good for you to let that dirt build up.
2. Always do the counter tops and fans before the floor.
That way, you can brush whatever extra pieces you find on those areas onto the floor so when you sweep, you'll pick it up. This gives you a little less work, but still getting the full effect.
3. Don't ignore the corners and windowsills.
The corners and windowsills are the grossest areas of your apartment. Even if you're a super clean person, if you ignore these spots, it'll build up. It's good to just give the blinds and sills a quick dust and a wipe down. It'll be nice to be able to have the windows open and clean. Also, corners get ignored often and gather the most dust. Don't overlook them.
4. Buy a multipurpose cleaning product.
It's cheaper to buy one product rather than four and it can be used on all surfaces in your apartment. Make sure it's nothing toxic and that it won't ruin wood, if you have any in your place.
5. Swifter Sweepers are the bomb.
These babies fit into all kinds of areas. It's great to know your floors are super clean and that you didn't miss any spots. You can walk around your apartment barefoot again and know you aren't going to have dirty feet. Let it dry before you walk on it though, or you'll have a footprint on the floor.
6. Try not to wait more than two weeks to clean.
Even if you're not doing a full fledge cleaning, at least wipe down the counters in the kitchen and bathroom every two weeks or so. It's hygienic and will make it easier for you when you do the full clean.
7. If you have a pet, give it a bath the same day you clean.
Pets shed and make the apartment dirtier than it should be. If you bathe your pet on the same day that you clean, it'll give you a few extra days of a nice smelling, beautifully clean apartment.
8. Make sure to clean out the vacuum before using it.
Most vacuums can get clogged up from all the dust stuck inside. Make sure you empty it out before using it so that you know it's picking up everything it should be.
9. Wash everything.
Since you're already doing the cleaning, you may as well throw the towels and sheets into the laundry while you do it. Killing two birds with one stone as people say. If you do them both at the same time, you won't have to take another day to wait around for your laundry. Side note: you should also clean out the lint that gets into the dryer before use. Your clothes will dry faster.
10. Do a check before you call it quits.
Sometimes, you may overlook something and think it's clean, but it isn't. Do a quick walk through before you jump in the shower and make sure that you didn't miss anything. It can be super annoying to think you're done and then remember you forgot something.