2001 S60 Volvo Engine Mount

There are actually four mounts. The two on the passenger side are called motor mounts. The two on the driver's side are both called transmission mounts. I've included two photos of what yours will look like. The top photo is the right side upper motor mount. before ordering inspect the upper mount for a broken bolt. The bolt in the center sometimes breaks.

You have to remove the plastic cover on the valve cover and then you will be able to see the bolts holding the upper mount on. The rest is self explanatory.

Remove the two bolts that hold the cross bar on each strut tower. 4 in total. Remove the bolt that goes through the mount you will need to hold the nut or bolt while turning the other. Put the cross bar aside and unbolt the mount. Remove and replace and reinstall the cross bar.

if it moves alot but no clunking, probably a worn bushing. If clunking, bushing worn right out, or mount broken.

It is not that Hard, you can use the Jack from your Car... Lift up a little on the Oil Pan with the Jack, you will see the engine Mount move. Once you have that pressure on, then you just take the center bolt and then the mount bolts. Install the new Mount and lower the jack.

YOU DO NOT WANT TO LIFT THE CAR, JUST GET WEIGHT OFF THE MOUNT

Is the knocking a regular rhythm that is proportional to the speed of the car? Driveshaft center bearings generally drive you crazy with buzzing and grinding before they get to the point of knocking, but I suppose that is possible. Drive shaft and rear end bearings would not make noise as you start the car, however.
Is the knocking related to road surface or braking, and is it directly below your feet? If so, it is the control arm bushing. That part is bolted to the bottom of the car directly beneath your feet and it will knock when the rubber part fails and crumbles out. This is common on a car this old, but this part also would not knock as you start the car.
A knock when you start the car is more likely the exhaust pipe hitting the bottom of the car. This can happen if a bolt is missing from a hangar, or the pipe is bent, or an engine mount is broken. The engine mount on the passenger side is the easier one to see from the top, and is usually the one that breaks first, as I recall. I always suggest that engine mount replacement be left to professionals. That job is a good way to loose a finger.
Be sure and check the bolt in the bracket right at the rear of the engine. For some reason, this one works loose and the bolt falls out. You have to crawl under the car to see if that bolt has fallen out.
Another suspect is the transmission mount. Does the shifter move as you step on the gas and let off the gas?

There are 3 engine mounts that keep the engine steady and transfer the torque to the transmission. One solid mount on the front, and a hydraulic mount on either side of the engine. Worn mounts will cause sloppiness and difficulty in shifting, and noticeable play when pressing and releasing the accelerator.
The front mount, also known as the snub mount, is a rubber or polyurethane bushing that centers the engine in the engine compartment. This is a common wear point, and causes vibrations at idle when misaligned or worn out. Since your car is several years old, it would be a good idea to replace it and is a fairly easy operation (2/5 on the difficulty scale).
The mount should cost around $8-12 for a stock type mount, and around $35-40 for a high-performance polyurethane bushing. The upside of the high performance is that the engine pay is greatly reduced; the downside is that there is more likely to be slight vibration transferred to the engine compartment at idle, which is what you are trying to avoid. Unless you are a "spirited driver", I would suggest that the stock type mount (looking a bit like a mushroom versus a topless cupcake) should be just fine.
If your car is running rough, then you should really look into a tune-up before starting the installation, as adjustment will be difficult is the engine isn't running smoothly. On these cars, new plugs and air filter, as well as vacuuming out the airbox pre-filter of leaves, dirt and bugs can do wonders for a smoother idle. (The next level of sophistication is cleaning the Mass Airflow Unit, but that's a more extended topic.)
Here is the process for installation: Raise up the vehicle on wheel ramps or with a jack and sturdy jack stands. DO NOT EVER WORK UNDER A VEHICLE SUPPORTED BY A JACK, USE THE JACK STANDS. You can get the jack stands for under $30, and your life isn't worth taking a chance. While you are being a good mechanic at the deep end of the gene pool, put on goggles or safety glasses. There is greasy dirt that WILL fall in your face, and it will get in your eyes, believe me it is nasty.
After the car is fully supported, take off the splash shield, which is held on with several quarter-turn screws. You might want to take picks with your phone or digital camera during the whole process to be confident on alignment.
You should have a good flashlight or worklight. While you're under the car, inspect for oil leaks, and peek up at the motor mounts on either side of the engine. If you see an oil dirt at the bottom of these mounts, they are likely worn out and should be replaced. That's a bigger job, probably about $500 at the dealer, $120 at home with the right tools and half or a full day of your time. But you can still replace the snub in the front independently, so don't give up.
There are three bolts on the front lower engine mount at the front of the engine. You can now see the mount protruding into the front rail of the car. Remove these 3 bolts. (Don't worry, they center the engine, they don't hold weight.)
You can now remove the old rubber snub mount. Clean the mounting post, and press on the new snub to the aluminum engine mount. This may require some force and may be helped with a little silicon grease or soapy water.
Next loosen the four nuts holding the snub basket to the front clip. (Do not remove, but leave hand-tight as these will facilitate adjustment.) You can now reinstall the lower engine bracket onto the engine and tighten the three allen head screws.
Adjustment: Start the engine and let idle for about a minute, popping the accelerator a few times to help center the snub and the receiver. Let idle for 10 seconds more without touching the gas, and turn off the engine.
Back under the car, tighten the four receiver nuts without moving the receiver. Start the engine back up, and check to make sure there isn't any unreasonable low frequency vibes transferring to the car. (Assuming you did the tuneup.)
Finish up by ensuring that all nuts and bolts are properly tightened, reinstall the splash shield and screws, and lower the car back on the ground.
Take the car for a test drive and see if it solved your problem.

have they checked the sway bar stabilizers,or if a lower control arm bushing has moved out of place.or maybe a strut bushing and mount

are you sure its coming from the transmission?check your torque mount on the driver side of the motor,the one on the top,see if the bushing rubber is cracked or broken

Remove the wire connector from each horn and attach a voltmeter or test light. Have a helper push the horn button while you check for voltage. If there's no power getting to the horns you have to work your way back to the relay checking for shorts. If there is power try holding the horns metal mount against a good ground like an engine bolt or the sub frame. And with wire reconnected have your helper try the horn again. If it sounds then clean rust away from mounting bolt and car (rad support or grill bracket), and look for a loose or broken ground strap to the rad support (from either the battery or engine). If both horns still don't work either they're clogged with snow or dirt (bring them inside to defrost or clean out), or they need to be replaced.