This article will discuss what to measure, how to measure and values to compare for physical fitness.
All metrics listed here can be easily measured at home without specialized equipment, yet should still give a fair picture of your overall physical fitness.
Typically physical fitness is measured in 4 dimensions :
Aerobic fitness : defined as the cardiovascular system (circulatory and respiratory systems) to supply oxygen during sustained physical activity.
Muscular strength & endurance : muscular strength is the ability of a muscle to exert force while muscular endurance is defined as the ability to perform repeated contractions against submaximal resistance. Strength and endurance may be measured separately, however here we treat them as the same thing.
Flexibility : defined as the range of motion of a joint.
Body composition : defined as the relative amount of fat, muscle and bone as well as other components of the body.
Other dimensions of physical fitness could be : (this article will not suggest metrics for these dimensions)
Balance : abitlity to keep equilibrium while either moving or being still.
Coordination : how accurate and smoothly senses and body parts can coordinate to perform motor tasks.
Agility : how fast you can change position of your body.
Power : maximum force in minimum time.
Speed : maximum movement in minimum time.
Stamina : anaerob capacity (based on phosphagen & glycolitic as opposed to oxygen)
Accuracy : control of movement in a given direction at a given intensity.
Reaction time : the time between stimulation and the beginning of an reaction.
Ok, lets get started.
Aerobic fitness measurements :
Test RHR (Resting Heart Rate) : for 10 years and older the resting heart rate should be between 60 & 100, however in general the lower the resting heart rate is the better your fitness and in general your RHR should not be above 80, some elite endurance athletes can have a RHR below 40. 
Test HRR (Heart Recovery Rate) : of all the physical fitness metrics in this article HRR is the most difficult to measure. Find a box (chair, bench, stairs) approximately 45cm height and step up and down for 3 minutes approximately 24 times per minute (faster if less than 45cm height). Measure your heart rate immediately then finished (over 15 seconds and then multiply by 4) - this should be in your Target Heart Rate range (see table 1). Rest 1:30 minute and then measure your heart rate again (over 30 seconds and then multiply by 2). Your heart recovery rate, HRR, is the first measurement minus the second measurement and is a metric for how fast you recover.
Table 1 : Target heart rate based on age 
Table 2 : HRR norms for 2 min rest based on age 
Muscular strength & endurance measurements :
Test pushups : how many perfect pushups can you do without a break depends on your age : pushup is an important fitness metric as it is closely related to heart diseases .
Test plank : how long time you can hold a plank :
Table 3 : Pushup norms for men 
Table 4 : Pushup norms for women 
Table 5 : Plank norms for men & woment all ages 
Flexibility measurements :
Test sit-&-reach : tests flexibility of lower back and hamstrings. Sit on the floor without shoes and your legs straight out from your body, the back of the knee firmly pressed against the floor. Place one hand on top of the other and slowly reach forward until you cannot reach further. Measure the distance between your finger tips and the sole of your feet. If you can reach further than your soles, your distance is positive. If you cannot reach to your sole, your distance is negative.
Test groin : tests flexibility of the groin. Sit on the floor with your knees bent and your feets flat on the floor. Let your knees fall outward as far down to the floor as they can while your soles are facing each other and hold together. Grab on to your ankles (one hand for each ankle) and pull your feet inwards as close to your groin as possible. Measure the distance from your heels to your groin.
Table 6 : Sit-&-Reach norms for men & woment all ages 
Table 7 : Groin flexibility norms for men & women all ages 
Body composition measurements :
Note that body composition is a non-performance metric, however I think it is still relevant as a measurement of overall fitness.
Test WHR (Waist to Hip Ratio) : calculated as the measure of the waist circumference (just above the belly button) divided by the hip circumference. Eg. my waist is 114 cm and my hip is 106 so my WHR is 1.08.
Test BMI (Body Mass Index) : weight to height ratio calculated as you weight in kg divided by the square of you height in meters, eg. I weight 102 kg and is 1.86 m height, so my BMI is 102/(1.86x1.86) = 29.5. While BMI is a poor measure of how fat you are it is anyway commonly taken as a measure to estimate if you are at a healthy weight, underweight, overweight or downright obese (like me).
Table 8: WHR norms for men & women 
Table 9 : BMI norms form men & women age +20 
My own personal test :
Ok, it is time to take my own medicine, here it comes :
RHR (Resting Heart Rate) : 82 - not within 60-80.
HRR (Heart Recovery Rate) : 120-90=30 - biological age about equal to actual age.
Pushups : 10 - average for my age.
Plank : 1:50min - average.
Sit-&-reach : -16cm - poor.
Groin flexibility : 16cm - fair.
WHR (Waist Hip Ratio) : 1.08 - obese.
BMI (Body Mass Index) : 29.5 - overweight (bordering obese)
The above is just some ideas I got off the internet, you are welcome to suggest other ways to measure physical fitness in the comments or even post your own physical fitness metrics.