How do I install the compression ring into the cylinder of a sears model # 919165140?

They mean if you run it then remove it.

It can vary between make and model of car. However, a general rule of thumb is that 135+ average is okay. Less than 85psi is pointing at something seriously amiss in the engine.

It can vary - some cars may have 125psi as 'average' compression.

Don't expect each cylinder to give the same compression reading as there will be a fluctuation. Another general rule of thumb is that there shouldn't be more than 10% variation between the readings. That is, if cylinder No1 is 135 psi, cylinder No2 shouldn't be less than '125 ish'.

If you suspect you may have compression issues, it's quite easy to do a bit of fault finding. Warm the engine first so that the pistons are expanded in the cylinders. Then do a dry compression (normal) test.

Here's some examples of compression tests on a 4 cylinder engine:
130 127 129 127

All compression readings are within 10% of each other. Fine.

Example 2:
95 95 129 127
Here, a low compression reading on cylinder 1 and 2 suggests a problem. It may be due to a faulty head gasket/cylinder head allowing compressed gases to be transferred via the defective head gasket from one cylinder to another.

Example 3:
130 80 129 127
Cylinder No2 has a problem. It's compression is way down. The other three cylinders are fine. So .. what is the cause of the low compression on cylinder 2? It could be a broken ring/cracked piston or a burnt exhaust valve.

This is where you do a second compression test - called the 'wet' test.

Squirt some light engine oil into each cylinder. Aim for the cylinder walls so that the oil can find its way down the walls and around the piston rings. Place a rag over each spark plug hole and spin the engine to expel excess oil.

The oil that you have sprayed into each cylinder will form a 'seal' around the piston ring. Do another compression test and note down the readings. Here's example 3 again:
Example 3:
130 80 129 127
.. with the low compression on cylinder 2.

If after carrying out the 'wet' compression test you have a reading along the lines of
130 100 129 127
suggests that the bore/piston rings in cylinder 2 are at fault. The compression has increased on No2 cylinder because of the oil forming a seal around the rings.

If there is no increase in psi on the wet test i.e
130 80 129 127
This suggests a burnt exhaust valve.

if it is a water cooled engine the ring gap at the bottom of the cylinder should be around .010"
rings have to be installed the correct way up or the compression doesn't help push the rings against the cylinder walls for effective seal
piston skirts will touch the cylinder walls as the pressure pushes the piston to one side as it pushes the piston back down the cylinder
I have to ask did you put an old piston back in the new cylinder
was the new cylinder standard size or over size
what was the ring gap before you fitted them to the piston
did you use new rings or the old ones --maximum rin gap is .025"
rings don't wear in , just wear out
why did you replace the cylinder in the first place
was it because of low compression or taper wear
as silly as all this seams it is all very relevant to your question

What you need to do is lift the car take out the wheel where crank shaft is,
also know as the harmonic balancer

when you do your compression test squirt some oil in the cylinder through the spark plug hole first then check compression if you have compression then its rings. If still no compress you might have worn off cam lobes.

The compression is low. This indicates bad piston rings. The cylinder may look okay but chances are the cylinder wall has low spots. I suggest you have the shop bore the cylinder and install a first oversize piston and rings. Since the head is already off, I would re-seat the valves and install new valve guide seals. With proper compression the bike will be noticeably stronger.

low compression in one cylinder usually indicates a bad exhaust valve. Low compression in two adjacent cylinders typically means you have a bad head gasket. Low compression in all cylinders would tell you the rings and cylinders are worn and the engine needs to be overhauled. If compression is low in one or more cylinders, you can isolate the problem to the valves or rings by squirting a little 30 weight motor oil into the cylinder through the spark plug hole and repeating the compression test. The oil temporarily seals the rings. If the readings are higher the second time around, it means the rings and/or cylinder is worn. No change in the compression readings tells you the cylinder has a bad valve. have a good day!

The engine timing being faulty would be a very likely reason especially if all the cylinders have no compression. Less likely reasons could be forgetting to install a cylinder head gasket, putting the wrong size valves in the cylinder head, installing new valves without lapping them into the valve seats, loose spark plugs, and piston ring gaps that are lined up instead of staggered.

It's not worth the expense and time, just purchase a new one.

This is called blow-by. Start with compression test to find out is rings are ok. Need more information like gas diesel, model number of engine. So here is a general run down. Compression is getting into crank case. Several things can cause this. Possible causes are bad valve guides, rings, head gasket valve stem seals. Compression test will tell if low cylinder. If this is ok for your year model look to valve stem seals. If two cylinders next to each other low. Possible head gasket leak. Use compressed air 60-90 psi and listen were air is going. If blowing into crank case or intake exhaust manifolds. If crank case rings if not valves. I am going to assume your engine is burning oil or using more then normal. Possible white smoke from exhaust. If this is the case and compression is good valve stem seals should fix it. Hope this helps. Remember when compressing cylinders have both valves closed on top dead cylinder.