To take long exposure photographs it is important to line up your telescope as accurately as possible, parallel with the line round which the Earth rotates, and the simplest way to do this is Drift Alignment.
It’s simple but can be time consuming, dependant on how accurate you wish to be.
You’ll need a short focal length eyepiece (giving 200 magnification or more) with crosshairs, you’ll be deluding yourself if you think you can do it without one, and an illuminated reticule would be much easier to use.
You will be working with two stars, one in the east and the other in the south, and both should be within about 5° of the Celestial Equator and bright enough to see clearly at 200x magnification.
You will be allowing the telescope to track the star and be making mechanical adjustments based on what you see it do in Declination, ignoring what it does in RA.
Your mount’s hold down bolts should be firmly secure, not slack.
Go to your southern star, within about half an hour of due south.
Orient the lines of the crosshair up and down, parallel to the Dec and RA directions. Set the star up on the crosshair, and watch to see what it does.
You should see movement within a few minutes, in seconds if badly aligned to start with.
Ignore what it does in RA, but note which direction it moves in Dec., up or down from the RA line.
If your star drifts up, adjust the Azimuth knobs to move the star to the left in the eyepiece field.
If it drifts down, adjust the Azimuth to move the star to the right.
Then retighten the hold down bolts snugly, reset the star on the crosshair again and repeat.
Keep repeating the process till the star stays on the RA illuminated line for at least 10 mins.
Aide memoire? "Left-up in the air". Or "Down-right stupid".
When happy with that step, reset the telescope to your star in the east, again near the Celestial Equator, some 20 to 30° up.
Set it on the crosshair, again with the Dec line up and down and the RA left and right, and watch for up or down movement.
If it drifts up, adjust the Altitude knobs to move the star down.
If it drifts down, adjust the Alt. to move it up.
Then retighten the hold down bolts, reset the star on the crosshair again and repeat.
Keep repeating the process till the star keeps on the RA illuminated line for 10 mins.
When happy with that, repeat the process with the star in the south to make sure your adjustment in Altitude didn’t affect the Altaz settings.
Brian