This is the parable of the dishonest manager, about to sacked for squandering his master's property. (We don't know if used the property for personal gain, or made bad investments, or what have you.) The manager secures his future by slashing the bills of his master's debtors. As the old joke goes, he made friends in low places.
Jesus says: "Make friends for yourselves by means of dishonest wealth [mammon] so that when it is gone, they may welcome you into the eternal homes."
The story is clearly rich in irony: the bad manager saves himself by becoming an even worse manager. But does Jesus's conclusion rise (or perhaps sink) to the level of sarcasm? In other words, how am I to understand what Jesus is saying specifically about mammon?
Update (previously posted outside the question as fodder):
In long form, here are some of the readings and questions that it would be helpful to have clarified by an interpretation aligned with doctrine:
Taken as straight sarcasm (an oxymoron): "Go ahead, use money to make friends, and when it's gone and you're gone, then you'll know who your friends are. No doubt they too have a mansion of many rooms, and you can take the guest house by the pool."
Taken straight (albeit also with irony): There is a use even for money, and how you use it can, guess what, buy your way into heaven. (Obviously there is no quid pro quo, so it's not as crude as that.)
This is a different policy from "render unto Caesar," and is closer to the rich man who followed all the commandments but could not give away his wealth (any more than the camel could squeeze through the needle's eye). That is, there is a direct call to dispose of wealth, but how does making friends enter into it?
The policy position is laid out in the rest of the passage: you can't serve God and mammon, you must love one and despise the other. But you must be "faithful" with mammon, that is, trustworthy with it.
What does it mean in this context to be faithful with mammon, a very little thing? Jesus doesn't seem to be talking about tithes or donations to good causes or avoidance of greed (cf Luke 12). Nor is he talking about money management per se, putting coins in a bank to learn deferred gratification. In particular, the dishonest manager was praised for acting shrewdly, "for the children of this age are more shrewd in dealing with their own generation than are the children of light."
If this shrewdness is just a kind of carnal wisdom, a sophia of mammon, can we take this praise at face value? If the master who praises the manager is the Lord, as usual in these parables, then perhaps it just means that you have to cut the children of darkness some slack. But it's a backhanded sort of praise at best; Jesus is telling his disciples, But don't you children of light go acting that way. What is this shrewdness? Knowing whom to buy off? How big a discount to give? Maybe that's why the children of light must go whole-hog and give it all away. Otherwise, they'd just get taken.
Even in this view, I'm not sure which of the first two conjectures is more stable: that his crack about the proper use of mammon to buy friends and influence or at least grease the pearly gates is sarcasm of a high sort, or that his crack about the proper use of mammon reveals the deep irony in pursuing Christian ideals when dealing with our own generation.
Note: @AffableGeek's link to a broader bounty question is fruitful. A recent comment suggests plainly that Jesus is being sarcastic; there are interesting suggestions that the discounts dispensed by the manager represent his own cut, i.e., what he was skimming from the accounts, so that maybe he had learned to sacrifice money for more enduring relationships; there are suggestions that Jesus does mean for the children of light to learn from the worldly; and also a suggestion that the text is corrupt.