One of two things are going to happen. Either there will be a no deal Brexit, or there will be a second referendum. There are no other possibilities with the timescales involved here. The referendum is already getting close to impossible due to time constraints, but the EU has said they would extend the deadline if a second referendum was being held, so I think it's still possible. Anyone who thinks there's another possibility at this point is fooling themselves. So there's no point in asking what the "best way" to leave the EU is.
That said, while I'm an American and thus not directly affected by it, I do care about the UK on some level so for their sake I hope there's a second referendum. Specifically, I hope there is a second referendum that has ranked choice voting, allowing people to choose "No Deal", "May's deal", or "Remain" and I hope "Remain" wins. Now that people understand much better what leaving would entail (either no deal or May's deal, the latter of which would only be possible under a referendum like this anyway since it was already voted down in parliament), the people will be better informed, and the result this time will be indisputable. Every citizen that votes will have as full an understanding as could be reasonably asked for exactly what each choice means. I don't think there'd even be need for time to campaign, just enough to organize the vote and advertise that it was happening.
With ranked choice voting, if Remain loses again, Remainers can choose whether they'd like No Deal or May's Deal as their second choice, so they'd feel like they had at least some say in their future even if they didn't get to remain. I've seen opinions from Remainers on both sides of this debate, some saying May's deal is so bad that no deal would be better, and some still maintaining that any deal is better than nothing. So that would be at least a little more fair than simply leaving however the UK's incompetent parliament manages to. While I'd personally love to see Remain win, I'd still be happy for the people of the UK if they voted for No Deal under these circumstances as it would be a fully informed vote, as democratic as I can imagine it being.
Even the No Dealers and May's Dealers would benefit here, as there are some who would rather leave in some way, shape, or form even if it isn't their preferred way, and there are some who would rather remain than have a Brexit they don't want. I've seen all of these opinions expressed at least once since the first referendum, and a second referendum where all three are a possibility and people get to rank their preferences is much more fair than a simple yes or no vote. A ranked choice referendum would be the fairest way to do things, in my opinion, because not only is it more democratic, it's just a better, more legitimate referendum, that more accurately takes the people's opinion. So the people saying that a second referendum isn't fair because they're afraid their first referendum would be invalidated, the truth is that it wouldn't. In fact, the most likely outcomes would be a very similar number of leavers and remainers voting for a leave option or the remain option respectively for their first choice, likely not changing the outcome there, but with some possibility of the second choice coming into play and deciding what kind of Leave the UK really wants, or if the UK as a whole feels torn on leaving and only wants to do so if it can leave a certain way. I suppose there's also a chance that Remain would get over 50% on the first round and thus make the ranking unecessary, but I doubt it, honestly. If it did, it would be really close, but hopefully the second round would still be counted anyway so that the UK would get to see exactly how much consensus is formed by the second round. For all you know, maybe once the second choice is selected, one choice will have a supermajority, and the UK will feel a bit better about their choice since it wouldn't feel as much like one half the country dragged the other half into something they hated. I'd imagine that such a supermajority would be possible for any of the three choices.
As I said before, I'd be cheering for Remain, but like I also said, I'm from the US so it's not something I directly have a stake in. But I hate seeing you guys so torn up over it, so if anything, I'd prefer any outcome of a second, ranked-choice referendum to simply crashing out with no deal when you run out of time, or parliament miraculously deciding on a deal that the EU also accepts before the deadline (or an extended deadline, since the EU also said they'd accept an extension until the European elections so long as the UK had a direction they wanted to go in during the extra time that could arrive at a new deal). The latter would happen too fast and leave too many unhappy, and splinter the UK further, and no deal would make Remainers and anyone that wanted some kind of deal unhappy and generally make everyone feel hopeless, like they can't count on their government at all, and even the hard Brexiteers would be mad that all that time was wasted arguing over a deal when trade deals could have been worked on and prepared in time to be ready so that when Brexit happened the UK had a system of trade deals already in place. The second referendum, if it is ranked choice, just seems like it would have the most potential to make the most people happy, while the current course is by all accounts a disaster and making as many people as possible unhappy.