If you're only getting to it now, then you're picking it up from the used bin or in TPBs. Still, Batman RIP and its associated titles had a confusing interrelation, so this post will lay it out straight.
Let's say you're wondering in what order to read the associated stories. That has two possible answers. One, the order in which the stories were published. Two, the chronological order of the events. These two answers are quite different because stories set after RIP were published before RIP had ended. For those of us reading the stories as they were published, there were some mysteries (most notably: was the Batman in Final Crisis #1 Bruce Wayne or someone else?) and some giveaways (for example: Jim Gordon's appearance in Outsiders nixed some theories that he might have been the villain of RIP) that you just wouldn't even contemplate if you read the stories in chronological order. However, I don't think those mysteries were really intended by design -- they just happened, even though Morrison tried to play up one of them while the stories were being published.
Batman #156 (Robin Dies At Dawn) and other stories that will be collected in Batman: The Black Casebook. This stuff is for completists only: You don't actually need to be familiar with these to get RIP. If you were going to read one of these stories, it should be Robin Dies At Dawn. The gist is that Morrison took a number of old stories, from an era that all recent writers have ignored, and pronounced that these stories did take place early in Batman's career, but with different explanations for them than had been offered in the original telling. Mainly that Batman had been the victim of mind control and hallucinogenic experiences brought on by his enemies' various gases. Other stories in The Black Casebook show the original introductions of the Club of Heroes characters, which actually aren't that weird at all (The Black Casebook was supposed to be about weird things), but do play into RIP very, very peripherally. I read these stories and more looking for clues to RIP, but in truth, there are none there.
Grant Morrison wrote Batman into two issues of "52". These are effectively the beginning of his run on Batman, having been printed while the post-Infinite Crisis "Face the Face" storyline was running in Batman and Detective. They show two attempts Batman made to cleanse himself of angst and anguish. On a factual level, these are not essential reading for RIP, but they do establish important themes. Namely, the supernatural (in #30, Bruce undergoes a ritual in which some mystical Ten-Eyed Warriors in the Sahara cleanse him, apparently literally, of demons), and the psychological (in #47, we see a very brief account of Batman partaking of therapeutic isolation in a Buddhist "thogal" experience).
Batman and Son
Issues #655-658 focus on the introduction of Damian, the son that Bruce and Talia apparently have, but key clues to and plot elements of RIP begin to appear. We see one of the Replacement Batmen, some "Zur En Arrh" graffiti, and Bruce meets Jezebel Jet. Some details here and elsewhere led people to suspect Alfred as the villain of RIP. The first half of the first issue, showing the Joker being apprehended, is really not about "Batman and Son" at all, and is for my money, some of the best Batman storytelling there's ever been.
The Clown at Midnight
"The prose issue", #663, is a standalone Joker story, but introduces some clues and red herrings (which are a kind of clue) to RIP. We see the "red and black" theme introduced (and it is a clue to this particular story), and the colors of the Zur En Arrh Batman appear in some of the narrative prose. The whole issue is perhaps authored by Bruce, as a notebook entry describing his case.
The Replacement Batmen
One twisted replacement Batman is a problem. Three are a pattern. In #664 and #665, Batman encounters the second of three, and realizes that a third one is out there, waiting. This creates the unmistakable feeling that a larger enemy is out there, waiting. Someone watching Bruce and Jezebel through binoculars.
This standalone, set in the future, shows what would happen if Damian were a darker, devilish Batman when his father has since passed on. Is it real? Well, I don't think DC is going to transition to this reality anytime soon. But Grant Morrison said that we will see some of the characters from this issue in his upcoming Batman and Robin title, and by process of elimination, that means the villains. This issue did have important clues as to RIP, and showed the Third Batman, Lane, to us before Bruce ever met him.
Club of Heroes
It's bound to confuse some people that this story, #667-669 was collected under the name The Black Glove, and indeed, it showed the villain of RIP operating from the shadows. It remains unclear how (or if) the plan executed here fits in with the general plan of RIP, but in essence, it showed us something of how the Black Glove operates (at least in his "day job"). The story reads like a mystery, but it is only partially solved by the end. We find out who the underlings are, but the Black Glove remains at large.
Resurrection of R'as al-Ghul
This crossover, including Batman #670-671 and issues from other bat-titles, is almost entirely skippable from the standpoint of RIP. It has about one line of dialogue that is echoed in RIP, but otherwise is basically an entirely separate story. For those of us who didn't know that at the time, though, it served mainly to exclude R'as as a suspect, because why would R'as be the villain of two back-to-back crossovers?
The Third Man
Issues #672-674 describe one night in Batman's life, but the constantly shifting frames of reference with multiple visions and blackouts, make it more like five or six stories. The third Replacement Batman shows himself, killing policemen, and saving Batman when he had him dead to rights. In flashback, we see Batman's adult encounter with Joe Chill. Numerous elements of RIP start to show up, including Bat-Mite and Doctor Hurt himself. I would say that these issues are essential to RIP.
A one-shot in #675 is a sort of calm before the storm: Bruce and Jezebel go on a date and action-adventure follows.
The six issues themselves, #676-681, are the main story. A short, but enticing scene in DC Universe #0 shows Batman trying to get some help from the Joker, of all people. In the RIP hardcover, that scene is inserted at the beginning. Although that scene was published before Batman #676, the encounter probably takes place after Batman #676 and before #677.
If I had an amnesia pill, I'd read RIP on its own and see what I thought of it without having read the precursors. It's hard for me to even imagine that, with so much material in the preceding issues (and historical stories) coloring the experience.
Final Crisis and Last Rites
These two stories take place entirely after RIP ends, although flashbacks in Last Rites (Batman #682-#683) precede RIP by many years, peppered all throughout Batman's career. Including some that aren't even really part of his past. Because they happen after RIP, they are really not essential to understanding RIP. That wasn't clear to us at the time of original publication, however, and some readers read the final issues of Final Crisis waiting for RIP truly to end. In reality, RIP ended in RIP, although Bruce's exit from the day-to-day DCU was only begun in RIP and became real in Final Crisis.
Final Crisis #1 and #2 precede Last Rites. Chances are, Final Crisis #3 and #4 also precede Last Rites. Final Crisis #5-7 take place after Last Rites although DC published Final Crisis #5 before Last Rites ended, technically giving away the ending.
A scene late in Last Rites shows that Bruce apparently came away from RIP entirely unharmed, clinching the result that he entered Final Crisis as more or less his plain, usual, wonderful bat-self.
Despite bearing the RIP logo on their covers, the crossovers in Detective, Nightwing, Robin, and Outsiders did not interlock with RIP at all. They were printed before RIP ended, and so were perceived as a source of clues. The ones set in the future showed us characters who were not the villain of RIP (by the dint of the fact that they were still walking around, free, and "good" after RIP ended). But otherwise, no clues at all.
In a nutshell, the Heart of Hush story in Detective took place either right before RIP or in the very early stages of RIP. But it has little to do with RIP aside from mentioning events in RIP in about two speech balloons. The Nightwing crossover is equally unrelated, but is set after RIP. By showing us Alfred, it gave away that the butler did not do it. I did appreciate a line in which Two Face expressed admiration for how the Black Glove had gotten Bruce. The Outsiders crossover was also set after RIP, and thus showed us more characters who likely weren't "it", including Jim Gordon. However, Bruce's absence from the world at this time, almost certainly before Final Crisis, is apparently a contradiction of Morrison's plotting that Bruce went adventuring with the JLA immediately after RIP. Most likely, Morrison's plans were not revealed to the crossover writers in full, but enough for them to know that, say, the Joker was again in Arkham after RIP.
Finally, the Robin crossover was a crossover, in the sense that it took place immediately during the main action of RIP, and reflected that action very directly, even showing us a picture of Batman as he was during the main events. It shows the effect of the event on Robin, but basically, the influence is one-way-only: RIP is necessary reading for these Robin issues, but the Robin issues are not necessary reading for RIP.
So that's how the issues relate. Happy reading, or re-reading.