The sky is a big place! In order to keep from getting lost, we need a sense of scale and direction. For typical naked-eye sky watching we use altitude and azimuth. These two coordinates are given as an angular measure in degrees (°). Altitude is measured up from the horizon, and azimuth is measured to the right from true north just like compass headings.
This is all pretty straight forward, but to be useful you'll need to get comfortable working with degrees of arc. The basis of this measuring system comes from a circle having 360°. Half a circle is 180°, a quarter circle is 90°, etc. It is impractical to think in fractions of a circle when so some other way of measuring degrees is needed.
As it turns out, we have an instrument that's always within easy reach. Certain positions of fingers are useful for estimating angular measure when held at the constant distance of arm's length. This works because whether big or small, our hands and fingers seem to have been made in proportion to the length of our arms.
One such configuration I find very useful is the index finger and pinky spread apart but not forced. For me and many others, this measures 15°. Some other configurations are: the pinky = 1°, three fingers = 5°, a closed fist = 10°, and the pinky and thumb spread out = 20-25°.
I have become so comfortable with and confident in measuring 15° that I usually just use it to visually estimate smaller measures. For 7° I can imagine the mid point between the two fingers, and can even do thirds for 5°. I can also use both hands, making the 15° spread side by side for 30°. Don't worry too much about precision. This is only to get you to within a degree or so.
Also, don't worry about what I say or something you read about what works. You need to find your own measurements that are comfortable and repeatable. Below are charts of Orion and the Big Dipper, two well recognized star patterns. Use some of the angular measures I've included to try calibrating your own finger combinations.
If you do want a bit more precision and great repeatability for some special purpose, you can make a sighting tube that has a known field of view. I made some out of cardboard mailing tubes of 2-inch inside diameter lying around. I calculated the necessary tube lengths using simple trigonometry in a freeware program downloaded from the Internet. I cut one tube to 11 7/16 inches providing a 10° viewing circle and another to 19 inches for 6°. I find the shorter 10° "instrument" more useful.
Azimuth is a little easier to deal with because we are more familiar with compass directions. I made the graphic below to quickly see the structure and degree ranges of the typically-used compass points. The named points are found inside the yellow ring with their azimuth inside that. On the very outside are azimuths corresponding to each point's 22.5° range. I find it useful to convert quickly between an exact azimuth and a compass point. For example, if you were looking for an object whose given azimuth was 239°, you would look towards the west-southwest.
All images are copyrighted by Frank Zullo. Please do not use without written permission.