Above is a pictogram of what a co2 laser cutter would look like without the doors, It should be noted that one should never look into an open laser cutter with the laser on without laser grade safety glasses. I am not responsible for anyone's blindness or other injury/ damage for any reason, now that that's out of the way lets continue. If you fire the laser and don't see any effect on your piece or if as your scanning side to side and its plenty strong in the middle but fades out at the end mirror alignment is probably the culprit. The following is the proper procedure in plain English.
Step 1: Adjustments
this is the mirror that is mounted on the x-axis rail, if you look at the back you will see 3 brass screws designed to adjust the angle at which the laser beam is reflected, you will find similar screws on the mirror at the back in front of the laser tube. you should also notice that the white bracket can slide side to side on its mounting screws, you should also find that the head that contains the focal lens does the same front to back.
Step 2: "but I Cant See an Invisible Laser Beam!"
And you shouldn't try to. Put a piece of masking tape over the mirror (the Chinglish book says to use double-sided sticky tape and cardboard but that makes it more difficult to aim) if you haven't already done so make sure your water pump is running and that there are no bubbles in the tube. CLOSE THE LID (and put those dorky glasses on) then momentarily press the test button and it should burn a hole somewhere in the tape. Be prepared for a rare but occasional flare up, you should be able to just blow it out if you get one but you should always have a fire extinguisher handy just in case. Once it's been adjusted you will need to clean the mirror with lens cleaner and a soft cloth.
Step 3: Lets Go
place a piece of tape over the mirror in the back by the tube and fire the laser, this one shouldn't need much adjusting just make sure it's in the center of the mirror. then clean it
Step 4: Next Mirror
move your Y-axis to the top (home) tape and fire and adjust the screws on the back of mirror 1 so that the beam hits the center of the mirror vertically, don't worry about horizontal yet.
Step 5: Move Back
Move your Y-axis all the way down and fire again, then see where the holes are and adjust the screws to where they land in the same place, move back to home and repeat until the 2 holes match.
Step 6: Center
slide the white bracket over to so the laser hits the horizontal center of the mirror, then clean mirror 2.
Step 8: Repeat
tape the head and move it all the way left (home) then fire the laser and adjust to vertical center.
Step 9: Move X-axis Right
move it all the way over and fire again, adjust the screws to where the 2 holes line up and slide the head forward or backward as needed to center horizontally.
Step 10: Clean
clean the last head mirror and lens if needed and your done
Step 11: What If It Didn't Work?
fist go back and make sure you're still centered on all the mirrors then it's more specifics
mirror 1 isn't centered, what do I do?
this varies machine to machine, some you can adjust the tube a little others you adjust the mirror position. If you have access to a 3D printer I recommend making this adjustable tube mount.
The slide adjustment doesn't move far enough?
I had quite the fight with this, I took mine apart and put it back together how I wanted it. while doing so I made sure the rails were in square as opposed to 1/4" out only to discover my mirrors didn't line up anymore until I sent it back out of square. I didn't like that so I drilled new holes for mirror 1 bracket and made a replacement head plate with longer screw slides
one final note, if your focal point looks oblong or isn't straight down its because your not hitting the center of the focal lens, this takes a bit of patience but to fix it you need to slide the head around until it looks round, it helps to take it out of focus (raised or lowered) to maximize the effect