It is certainly a good thing and also fun, to learn how to use a sextant. Even the US Navy realized this as they started to teach again the almost lost art of celestial navigation. However, to get a good star position fix requires a lot of training and experience. Start simple with ‘shooting’ the sun and plotting the position line on the chart. A radar bearing line for instance would help to get a fix. In this way you can immediately check the result with a GPS fix. You should improve your skills over time in this way. In due time you will also learn what your personal error is, well not everybody has one but most of us have.
The calculation method used until the 1980s was the Haversine Formula and Log Tables. Navigators on commercial ships used Sight Reduction Tables but most preferred the longer method in the interests of accuracy and flexibility. These days you can buy a pre-programmed Texas Instrument celestial calculator which simplifies the calculations enormously.
It is even possible to start the learning curve with a simple plastic lifeboat sextant.
This is my ancient sextant but still in excellent working condition with a very clear night glass.