The original (JLFox) instructions to do this are now printed further down on this page.
I found that half of the process described was unnecessary and confusing.
Found immediately below is the easiest method to flushing your tranny, along with helpful piccies.
   

You only need about 1 metre of hosing.  (I bought two metres and, as you can see,  it's obviously too long ... )

Now you're ready to start flushing.

Here's another quote from the method below, quoting the relevant bits.

Note: whatever you do just don't let the tranny run dry. Click here for brief info on the danger in letting your tranny run dry (see the first of the posts)

This won't happen if you stop the engine whenever bubbles are produced at the clear hose. If the hose is a snug fit, which it should be, the bubbles you see are definitely coming out of the tranny itself... and it's a clear sign that you should be stopping the engine idle & replenishing with more new ATF.

My slight change to the method:
During my ATF flush (that I captured in the pics that you see here), I did not put in ATF first.
I just turned on the engine, and waited for ATF to pump out the hose.
After a brief time (~ 1 sec) ATF started flowing to my 10 litre plastic gerry-can,
and I continued idle until I saw bubbles, after about 2.5 litres,
and I then switched off the engine.
 

I didn't see any sense in putting in fresh ATF at the start that would just get contaminated by the dirty stuff that we are trying to get out. So I emptied out the tranny (to the 'bubbles' stage) first, then I started replenishing (so as to not let the tranny run dry).

So after the bubbles appeared, I then put in 2.5 litres of fresh ATF and started it up again.  The funnel setup that I use to get the fluid in to the dipstick hole. (If you do this, make sure to always check the level of the smaller funnel so that it isn't overflowing, unless you enjoy great pools of ATF on your car and garage/driveway floor!)

Engine running, gerry can filling, and approx. 2.5 litres later, the bubbles appeared in the hose again.
I Switched off, and topped up another 2.5 litres.
Ignition on again, and by the time 7.5 dirty ATF litres were out, fluid from the out hose was now running nice & red.
Depending on the condition of the fluid you are changing, this might take a little more or less flushing.
You have to use your own judgement here; obviously when you see the same colour out as you are putting in,
the ATF inside the tranny could be safely said to be clean.
It can be difficult to see the outputted fluid as being clean: make sure you have good light behind the clear tube for the best judgement.

So once you are satisfied that the ATF coming out is clean, it's time to put the hose back on the cooler.
Then top up the ATF slowly, checking the dipstick, to get it to the right level.
Remember that the ATF fluid level is measured whilst the engine is idling, it's not like the engine oil level dipstick measurement which is with the engine off.

Do not overfill the tranny with ATF, this is a bad thing to do.

I make sure that levels are right by getting the fluid within the dipstick range.
Then I take for a ten minute drive to warm the tranny a little and check the level again.
Top up if necessary.

Quote from a post below:

Make sure that your clamp & connection to the cooler is OK while you're at it.
If you are using your old clamp and it is a little less inclined to bounce back, you
might want to put a strong plastic wire/cable tie around it for a little more 'security'.

Note that you have flushed everything but the cooler with this method. I don't believe it's necessary.
See post below by Dave or click the link on the tranny running dry & read the first post if you need consoling that this is OK!

Congrats, you have just flushed your ATF!

Note: I changed this ordinary dino ATF after just 11000 kms,
or just under 7000 miles. Call that overkill if you may, call me anal.
It gave a year of service, and some do recommend a change every year.
(However, I wouldn't bother doing it so often with Synth ATF.)
The oil did not look anywhere near as bad as it did when I
did the first flush at 57000 kms.
Then, it seemed very dark brown though its smell wasn't too bad.
I did it anyway (had to get these photos somehow ).
 

dipstick prior to change (11000kms old) click on thumbnail image for larger image	dipstick after flush click on thumbnail image for larger image
rag indicating colour of fluid after 57000 kilometres click on thumbnail image for larger image	rag indicating colour of new fluid click on thumbnail image for larger image

Older posts are here:

Another helpful message which added to one of my brickboard postings re. ATF flushing...

MESSAGE #10060486:  Re: Advice Needed - Flushing Transmission Fluid
     AUTHOR:  RussB <rbertrand02@snet.net>
     DATE:  Tuesday, 30 January 2001, at 6:07 p.m.
     Response To #10060465:  Re: Advice Needed - Flushing Transmission Fluid
     Author:  Michael in Sydney
     Date:  Tuesday, 30 January 2001, at 3:20 p.m.

I've done my ATF twice just as Michael describes. It works great. I suggest
getting a new hose clip (p/n 6842411, $3.10 list). 12 qts should be enough oil
to do a good job, 18 an excellent one.

BTW, ATF goes into the cooler from the top hose and exits out the bottom. If
you use the "official" Volvo method of flushing, you attach the clear plastic
hose to the fitting that is unscrewed from the transaxle.

RussB in CT

... posted by Dave the Volvo Tech  on Saturday, 18 November 2000, at 7:57 a.m.
...in response to "transmission fluid" posted by Andrew P.

                       Andrew-
                       The lower fitting on the radiator is the return. Due to access, I flush from the top fitting. I have made up a
                       hose with the fitting from a scrap radiator, so I don't know what size hose will fit. The retainer for the
                       hose is a spring-type clip that I spread with snap-ring pliers. I flush 6 quarts through the trans then
                       connect the line and add 3 quarts. Drive the car a few miles allowing all gears to engage and recheck
                       fluid level warm. Some cars take another 1/2 quart.
                      --
                       Dave the Volvo Tech

Thanks to "JLFOX, formerly jlfox" for this brickboard posting
on Friday, 1 December 2000, at 5:29 a.m. ...in response to
"Re: Transmission Fluid.....Now I Am Confused" posted by Eddie W. in FL.
 

                       Eddie,
                       This topic has been the subject of lots of discussion. You may want to check the archives. My advice to
                       a FL resident (heat) is to flush the fluid with a synthetic like Mobil 1. I've done this on 3 Volvos. The
                       first, an 850 because it was starting to get clunky. Volvo now has a service bulletin which suggests
                       flushing for various symptoms, including dark colored fluid and burnt smelling fluid. I fully agree with the
                       advice to do it every 30 to 50 K, depending on your driving habits, etc. It is a reasonable simple
                       process to flush yourself without getting under the car. I have posted the procedure outline and will do
                       so again below. I definitely am on the flush side of the discussion rather than drain and fill.
 

Below find a summary of the official Volvo flush method. I've done it and it works.

                       Car on ramps, blocks, jackstands, etc. *
                       Drain tranny fluid into pan. Plug is at bottom of tranny below axle and runs in same axial *
                       direction as axle.. Replace plug using new washer. 18 Ft lbs. *
                       Remove battery and tray to get access to top of tranny. *
                       (Air pump is mounted under battery tray.)
                       Remove hose on top of tranny by loosening nut. Hose is taper fit into tranny. *
                       Plug tranny hole. *
                       (Connect battery to car using jumper cables to avoid having to reinstall it) *
                       Fit clear plastic hose to reach drain pan over end of tranny hose. *

                       Add 2 qts of tranny fluid thru dipstick opening (I like the Mobil 1 Synthetic- used 11 qts total.
                       Tranny actually holds 8 qts so you're not wastiing much.)

                       Tranny in P. Idle engine until bubbles appear in fluid.

                       Repeat fill and idle cycle until fluid runs clean.

                       Replace hose, battery tray and battery. *

                       While idling, wlith parking brake on, run shift thru each position for 4-5 seconds.

                       Careful not to overfill tranny after last cycle.
 

                       I now recommend the alternate method which skips draining the fluid thru the plug and
                       battery removal. Instead disconnect the upper fluid hose at the radiator. Make sure you
                       have a spare retention clip as they have been known to break. Also have a 5 ft length of 3/4
                       or 7/8? ID plastic hose * and a hose clamp to put on the radiator fitting since that is where the
                       fluid will exit. All else is the same. Good luck.

OzBrick; * note also that 1/2" ID / 13 mm is the tube size necessary.