"Just" can act as an informal synonym to "only." You were right with that. For instance,
- I'm only looking out for you. I'm not trying to ruin your life.
- I'm only getting a drink. Not avoiding anyone.
- I'm only looking around. I don't need any help.
It can also be a synonym for "simply" in some cases. I've alluded to that in the comments, but it's worth bringing up explicitly. You could just as easily replace any of the *only*s in the above examples with "simply." You can use "just" to mean you're almost done ("just about done"). But these cases are a bit different from that.
I suspect the website is referring to something like this,
Person 1: Are you coming?
Person 2: Yeah, I'm just finishing a couple things up first.
That's the same as "only" here. "I'm only finishing this up, nothing more. So I'll be done soon."
On the other hand, as you just brought up in a comment, we can also say things like "maybe you should just go back to college." In a case like this, "just" is effectively meaningless. It's used to exaggerate the point. It's similar to "just about done" as was brought up earlier in this post--I can say "I'll be right there, I'm just about done," but that means pretty well the same thing, denotatively at least, as "I'll be right there. I'm about done." The daughter of your example could say "...maybe you should go back to college," but that just doesn't carry the same metaphorical punch as saying "maybe you should just go back to college." In other words, it makes the comment more serious and for lack of a better word, sassy. It gives the impression of severity.
Edit 2 (thanks wordsmythe):
"Just" can also be a relative term, denoting the choice or an acquiescence in favor of the simpler/easier option. In the case of "I'm just going to watch the game from home," "just" implies that there's another option available to do something more complicated or demanding than staying home (e.g., attending a party or going to a bar to watch the game). In the case of "Why don't you just go back to college" (see comments), there is an implication that the "you" might have a simpler or easier time going back to college rather than convincing the child that college is worthwhile. (Or perhaps that the speaker/child would have an easier time that way.)
This is with reference to a comment...
- "I just want..." -- This could be reworded in most cases as "I only want." You might say "I just want water" to a waiter, indicating in an informal way that you don't want soda. You could also take a more dramatic spin and say something like "I just want you to trust me!" In that case, it's emphasizing how easy the task is. In other words, "I only want you to trust me. Is that so much to ask?"
- "I just don't understand it" -- Here, and someone else might have a better, more technical explanation to this than I, it's mostly just, again, a way of emphasizing the point. "I just don't understand it" indicates a more, I hesitate to use this word, but an aggressive tone. It shows some frustration. The word "just" here doesn't really mean anything, it mostly just helps convey a certain tone. You could also substitute "really" here.
- "I just can't believe that ..." -- This is similar to the previous two. It's emphasizing the point. You could also say "I really can't believe that...."
- "I just don't get it" -- This is the same in every way to the "...understand it" case, even in meaning.
- "He just doesn't understand it" -- Same thing here, changing the subject doesn't change the meaning. "He just doesn't understand it. No matter what I do." Just to add to the confusion, you could also say "he really just doesn't understand it." That's just that much more emphasized.
- "I can't just..." -- "I can't just leave school to join the circus" (first example that popped into my head). Yet again, mostly emphasis. Here, it's emphasizing the outrageous nature of the request. "What? You want me to do that?! I can't just do that." I suppose you could take it as a sarcastic approach at the same kind of making-light nature we discussed earlier. "I'm just gonna watch a game first" is playing into the light-heartedness of the word, whereas "I can't just" is playing against it.
- "I just can't..." -- Same as the last one, although you could also take this to be extra emphasis in a different way. "I just [dramatic pause] can't!" Again, it really doesn't mean all that much extra, at least in a denotative way. It's just a way to enhance the phrase and make it seem more severe.
As for your point about how it can mean "only" or "really," I don't really have a rule-of-thumb to discern the intended meaning. Much of it is in the context or tone. In most cases, though, it doesn't really matter. I hate to say that, since it's a frustrating answer, but for the most part the ambiguities can be resolved through either context or ignorance. For the most part, though, just test which makes more sense. "I'm just gonna watch the game," does "I'm really gonna watch the game" make more sense, or "only?" I'd say "only." "He's just so frustrating:" "He's really so frustrating," or "He's only so frustrating?" Probably the first one. I'll try and think up a better answer for that, but yeah.