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Once the telescope is out of doors, you are ready to complete the alignment of the polar axis. How far you wish to carry this out is up to you. For instance, when I use my telescope from my porch, which does not permit viewing of Polaris, I just point the telescope towards the north. To rough align your telescope, just point it at Polaris. This is more than good enough for most purposes.
The purpose of polar alignment is to prevent the object from slipping out of the field of view as it moves along its concentric circle, which will eventually happen if alignment is not perfect. In my experience, even after only a rough alignment the object will stay in the center of the eyepiece for a few minutes at least.
After alignment you still have to adjust the declination and right ascension axes to bring the desired object into view. On most equatorial mounts there are scales for each of these axes, called setting circles. The declination setting circle runs from 0 to 90 and back to 0. The mount has both a clamp that may release the telescope so that it moves freely along the declination axis and also a knob to control the movement more gradually. The right ascension setting circle has a scale for 0 to 24. It too can be both clamped or released for free movement and also has a knob for gradual changes along the right ascension axis.
You will need to use both of the axes to find an object in the sky. Release the clamp for one axis, carefully move the telescope towards the desired object and then lock the tube so it is immobile. Now repeat the same process for the other axis. Releasing both axes at once makes control of the tube's movement more difficult.
Now is the time to use your "gun sight". Place your head behind the telescope tube and look through both of the sights that you mounted on the tub towards the sky. You may now unclamp each axis to point directly towards the desired object or use the adjusting knobs. One some mounts the possible movement along the declination axis while is clamped is quite limited and you will find it easier to release it first. Once the object is within your gun sight, it should also be found within the finder scope. Check that an eyepiece with a low magnification is on the telescope.
Using the knobs controlling the declination and right ascension, center the object within the eyepiece's field of view. Provided your telescope is roughly aligned, it will remain within the field of view as you slowly twist the right ascension knob. If the object quickly moves towards the side of the field despite adjustment of the right ascension, the telescope should be more carefully aligned. Otherwise, you just need to play with the right ascension knob and only very occasionally adjust the declination. In order to find an object too dim to be seen directly, first locate a nearby visible star and then star hop to the desired object.
Everything previously mentioned regarded averted version and dark adaptation when observing binoculars or the naked eye also applies to using a telescope. After going through all the expense and bother of obtaining a telescope to gather more light into your eye, why waste it? One difference between the use of binoculars and a telescope is that most telescopes utilize one eye at a time. Don’t close the other eye while looking through the eyepiece. Shutting one eye will cause the other one to squint. I sometimes cover the non-viewing eye with my hand to block out distracting light and have been thinking of trying a pirate-like eye patch, but haven’t gotten around to it yet.
You will probably want to bring all the usual skygazing accessories such as a red cellophane-covered flashlight, paper, pencil and possibly a chair to sit on. I always take with me an old blanket on which to kneel, which is sometimes the most comfortable position to look through a telescope. You will also need some sort of carrying case for eyepieces and other loose accessories. One last item that I strong recommend you bring is a regular flashlight.
Sometimes during an observing session you will hear a mysterious clink as small object, possibly from the telescope itself, falls to the ground. Use the bright flashlight to sweep the area while packing up. It's no fun searching for a tiny screw with a cellophane-covered penlight.
Possibly the most disconcerting aspect of using a telescope for a beginner is the inverted image. All reflecting telescopes display an upside-down image to the viewer. While some maps of the Moon are also printed upside-down for easy use, most stars atlases are not. There are eyepieces that invert the image to its original orientation.
An image inverter will absorb some of the precious light and it is better in the long run to get used to the inverted image. This is easier than appear to be at first. One evening I got out of my car and looked upwards at lovely half-moon near the horizon. There seemed to be something not quite right about it. Then I realized that I had become used to its inverted image through my telescope and it appeared strange because I was seeing it right side up.