It is not unusual for athletes to measure their heart rates when at rest and when training, and there are advantages to monitoring heart rates, but it is important to have some knowledge about various intensities of training and how tracking your heart rate can be of value, or misleading.
Resting heart rate is what you measure upon waking in the morning, while you are lying still in bed. It is best to take a count for at least 30 seconds, or for a full minute. You might take two 30-second counts just to see if you are getting the same value. At different times during the day it may also be a good idea to get a count while sitting still and relaxing, just to compare that number with your morning waking-up number. A pretty typical resting value will be about 72 beats per minute, but resting heart rates can vary tremendously from one individual to another.
It is typical for runners to compare their resting rates with other runners and when they have a lower value it is often assumed that they are fitter than the other person. This may or may not be the case. Values in the 40s (and even below that) are not at all unusual among trained athletes, but I also remember one World Record holder whose resting heart rate was never recorded below 60 beats per minute, so it is not all that clear that you must have a very low resting heart rate to be very fit. It is more useful to compare your resting heart rate with your own resting value during different phases of your training season.
If you are just palpating your heart rate (going by feel with your fingers or hand), then when exercising, it is best to count the rate for about 15 seconds and convert that number to a 1-minute value. Counting for more than about 15 seconds will not be as accurate since your heart slows down quite quickly when you have stopped exercising to take the count. Once you have practiced a few times you will find it quite easy to get a valid reading on how fast your heart is beating under various intensities of stress. Of course, many runners use a heart-rate monitor and that makes it a fairly easy job to check your rate at any time during a run or during recovery.
I would like to make you aware of the fact that maximum heart-rate values can’t always be determined using some formula that is related to your age. For example, it has been popular to subtract your age from 220 to get an estimate of your maximum heart rate, but this can be far from reality for some people, even though it may work well for others. I have measured a 50-year-old’s maximum at 192 and 220-50 = 170, so this runner would be under-stressing himself if using that 170 value to determine various training intensities. Another runner (at age 30) had a maximum heart rate of 148, and using 220-30 says his maximum should be about 190. Suggesting that this runner try to work at a heart rate of 152, in order to be exercising at 80% of his supposed 190 max, would not even be a possibility, no matter how hard he ran.
Heat and dehydration both can cause an increase in heart rate, so under these conditions of stress heart rate will be higher than expected for any particular speed of running. In summary, if interested in monitoring heart rate, try getting used to taking your own heart rate at rest and immediately at the end of some easy and moderate runs, and start keeping a log of 1-minute heart-rate values associated with different runs and also include the weather conditions with any exercise values. When later in the year you see lower heart rates for rest or for the same intensity of exercise, you know your heart is getting stronger and you are getting fitter.