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It's worth it to know in advance when buying a system if it includes a rack kit. If you're lucky, your system will come with one.   They typically cost something like a couple of hundred dollars each.  There are different rack kits for different Integrity models; read your manual and do some research before you buy.  Some models might have interchangeable kits, but in general, this is not so.

I'm using an rp4440 as an example.  Here's the server ready to rack, with the rack kit laying on top.
[[File:rack1.jpg|thumb|none|rp4440 ready to rack.]]

Take the rail kit apart.  There are basically 4 pieces.  Right and left rails that attach to the server, and left and right slides that attach to the rack. 
[[File:rack2.jpg|thumb|none|Rail kit taken apart.]]

The rails snap lock onto each side of the server.  They are clearly marked with "front" on one end.  That end goes to the front (duh).
[[File:rack3.jpg|thumb|none|Rails on the server.]]

Make some room in your rack.  Hopefully you have a matching post merger HP graphite (grey) rack.  These rack kits look like they'll go into any rack with rectangular holes.
[[File:rack4.jpg|thumb|none|Making room.]]

There's a right hand and left hand slide.  It's hopefully pretty obvious which is which; the open ends of the slides (the ends that take the rails) have to go towards the front.  The slides have these posts on both ends that fit in the (rectangular) rack holes.  
[[File:rack5.jpg|thumb|none|Posts on the slides.]]

The slides are adjustable in length.  My slides were about the right length.  The rear end will adjust (by slip fit) an inch or two in either direction.  Extend it to the maximum length.  Put the front posts in, align the rear posts with the right holes, and then collapse the slide so that both sets of posts, front and rear, are firmly seated into the front and rear holes.  (To radically change the length, you'll have to dissemble the slide and move to the proper sets of holes.  You probably don't need to do this.) There are 2 little spring lock catches (front and rear) that will lock each slide into place when you do it right.  No tools required.  (To remove the slide, you have to reach the little spring metal catch on each end on the outside of the slide and depress them towards the center of the rack.  Then the slide will come free of the rack).
[[File:rack6.jpg|thumb|none|Put the posts in the holes.]]

The slides look something like this when in place.
[[File:rack7.jpg|thumb|none|Slides in place.]]

Now basically you just align the server rails with the slides and stab it in.  Get two people, they are heavy.  Try to be gentle, that's sometimes hard when positioning something heavy.
[[File:rack8.jpg|thumb|none|Align the rails with the slides and push the server into place.]]

That's it!  Just push the server all the way in.  It will lock into place.  There are 2 catches on the front (right and left) to release it from the rack (to extend the server).  These depress towards the center of the rack.  The decorative bezel has little button things that make this apparent.
[[File:rack9.jpg|thumb|none|Server in the rack.]]

Hey!  You're racked.
[[File:rack10.jpg|thumb|none|A happy little racked server.]]