The reason LL grammars can't handle left-recursion or ambiguity is because those are both situations where the grammar has to make a choice based on something that it won't discover until the future. So they get stuck - the parser generator bails out with an error - or, frequently, a fixed choice is made for the grammar by the parser generator at the time the grammar is compiled into a table.
A GLL parser doesn't make any such choices: It takes all alternatives of the choice, building (conceptually) multiple parse trees - keeping the proper state in the grammar for each - and continuing through with the parse on each parse tree every time it reads a token. If, at any new token, one (or more) of those parse trees are invalid (the token can't be accepted by the grammar at that point): they're dropped. All which make it to the end are valid parses!
The trick, of course, is to do it in such a way that it isn't too expensive. A thing called a "Graph-Structured Stack" was invented for this (actually, for the earlier algorithm GLR). So, "proper" implementation should be able to achieve worst-case O(n³) time (size of parsed string). But in actual use, unless you're deliberately trying to confound the algorithm by trying test cases emphasizing left-recursion and ambiguity, you'll do much better - not far off from standard LL, but with relaxed constraints on the grammar. (Because in practice most ambiguities or left-recursion on actual inputs are resolved quickly, thus not many alternative trees are built and those that are don't last long before they're determined to be a dead end.)
(For a similar, easier to understand, problem: See the relationship between NFAs and DFAs when processing a regular expression. And there are plenty of good tutorials/blog posts on the internet explaining that.)
(For NFA vs DFA see the great tutorials by Russ Cox).
(BTW, I just found this recent master's thesis: "Exploring and visualizing GLL parsing (Cappers, 2014)". He claims to show how you can move incrementally from LL to GLL. It might help you. (If it does: report back!))