"A lot" is two words. "Alot" is not a word at all.
This might have to be a rule you just memorize with no tricks. Chant to yourself the phrase, "A lot is two words. A lot is two words," until you get it. Say it until you believe it! Say it until you know it! Say it until it bugs you just like it bugs me! If you need to, say it a lot!
Why? Because it is two words. It really is! See if you notice the pattern here:
Incorrect: I did aton of work today. Correct: I did a ton of work today.
Incorrect: I ate abit of dessert. Correct: I ate a bit of dessert.
Incorrect: I am alittle afraid of snakes. Correct: I am a little afraid of snakes.
Incorrect: I have alot of homework to day. Correct: You're an idiot and you are going to burn if you keep spelling a lot wrong, plus today is one word!
(I'm breathing, I'm breathing)
Okay, that is my soap box. These other cases don't put me in the mental house but I do see them from time to time.
Do it, breaking this rule will instantly and forever brand you as somebody who doesn't know what they are writing about