In addition to the definition in Grammar Wiki, I also find this table from Chinese Zero to Hero very useful since the separables （离合词）are grouped here by their HSK level:
@Audi-Mandarin-HSK_3 As far as I know, we are pretty much supposed to memorize these.
This is all very interesting. Didn’t know about 游泳 being seperable either! Thanks for the pdf @Ben-Mandarin-HSK_5 , Zero to Hero is such a great resource.
I also had a hard time with 睡著/睡覺/etc. I think of it in my head similar to what @Audi-Mandarin-HSK_3 said -
睡觉： sleep as a noun/to sleep/act of sleeping
睡着: fall asleep (“find sleep”)
睡不着：cannot sleep (“cannot find sleep”)
I just realised that in my head I think of 着 as 找 (even though they are not the same) hence why I thought of it as find sleep. So I guess this is not the most professional method but it made sense in my head 
Maybe because of the similarity in pronunciation. 着 uses the second tone and 找 uses the third so they are pronounced differently.
Wow a lot of good replies and you guys are correct.
At its heart 睡觉 is a separable verb like 学习
In spoken Mandarin most of the time people only say 睡 and leave the 觉 away because it’s just shorter to say. However in many situations whenever someone says 睡 your could also say 睡觉 it’s just a short form.
That’s the basic usage.
There are different sentence structures that also use 睡 (or 睡觉 if you have the extra time to say two instead of one character), which are made a bit more complex because two characters often used in that context are 多音字.
First the 觉 in 睡觉 is also pronounced Jue in 觉得 which is a completely different meaning and pronunciation and its important to keep them separate in your mind.
Second the construction 睡着 / 睡不着 means fall asleep / won’t fall asleep. The 着here is Zhao which sounds similar to 找 but this is accidental and the two characters have nothing to do with each other. Also the 着 is a 多音字 with another meaning and pronunciation and meaning zhe as in 站着，学着想着 etc which has nothing to do with 睡着 Shui Zhao. The character just looks the same but has a completely different promoinciation and meaning.
If you don’t want to worry about all the rules I wrote down the sentence structures 睡觉is usually used. If you know those you are ok for 95% of the cases
我 去/想/当 睡觉 (I go/want/am doing right now sleep)
我 睡 了 (I fell asleep)
我睡不着 (I can’t sleep)
and worry about the rest later. I never learned any of the rules for these but simply learned them by Chinese people using them and getting used to how they are usually used.
People in China speak a lot about sleeping, so there are plenty of opportunities to practice 
I second the point about just copying natives.
Personally I try not to get too hung up on grammar points and just listen to, and ask natives.
What they do I imitate and try to use sentence mining to remember (back to those post its sorry @Chloe-Mandarin-HSK_5 
)
For these reasons I have no idea how to answer the original question, but my personal advice would be not to get too hung up on the exact logistics and just imitate all the way.
(Probably terrible advice but it’s how I’ve rolled with it since 2017 
)
Me at 3pm, everyday
That’s a great example thanks for sharing.
The 一 is something you never really have to use as a learner. It slightly changes the feeling of the verb (睡觉） that is done in a more casual way. It’s a bit similar to adding “a bit” at the end.
Instead of “I want to sleep” its more like “I want to sleep a bit.”
This is quite a subtle difference that as a learner one can choose to also simply ignore. It means almost the same, just with a bit of a casual twist to it.
It doesn’t have a real translation into English, it’s “feeling” based. So one can safely ignore it and say 睡觉 oneself instead until one day one “feels” that 睡一觉 fits.
Similar to 睡一覺。。。 how about 睡午覺 
I hear this often 我要睡午覺. I actually originally thought it was 睡五覺 like, take a five minute sleep. But apparently not!
haha, @Max I think you belong in a Taiwanese company! here it is very normal to have a nap at lunchtime, I used to go into our partner company office in the afternoon and all the lights would be switched off and everyone asleep on their desks!
I’d love nothing more than to move to Taiwan!
To be fair I normally start at about 6am to align with China time, so I feel the occasional mid-afternoon power nap is justified 
That goes right along with 吃午饭
