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¿Cómo se siente? is used when speaking to people who deserve respect or for people you don't know.

 It's the "formal" way of asking the question.

      

¿Cómo te sientes? is used when speaking to people you know or to children.

It's the "familiar" way of asking the question.

    

If you are female, then your adjectives will end in "a".

If you are male, then your adjectives will end in an "o".

viejo - old (male)    vieja - old (female)

cansado - tired (male)   cansada - tired (female)

    

When "you" are the subject, the adjectives need to reflect your gender.

For ie. (male)

Me siento enfermo. - I feel sick.

For ie. (female)

Me siento enferma. - I feel sick.

      

     

The following adjectives don't end in an "a" or an "o", so they stay the same

for the male and feminine.

for ie.

fuerte - strong   

joven - young

triste - sad

for ie

(male) Me siento triste. - I feel sad.

(female) Me siento triste. - I feel sad.

    

The difference between Yo soy feliz and Yo estoy contento .
"Ser"(yo soy) is used when we are talking about a characteristic of the person: Yo soy abogado, yo soy presidente, yo soy feliz, yo soy rubio, etc
"Estar"(estoy)  is used when we are talking about a present feeling: yo estoy contento (now, but perhaps tomorrow not). 
Some people do say "estoy feliz" (especially in Latin America, in my understanding), but others consider it to be an error. (I imagine that in some dialects, "estoy feliz" is so common that using "ser" instead would be considered an error...) The supposed rule is that, for whatever reason, "ser" is always used with "feliz".
  

Feliz is used for a permanent happiness

and contento/a is used for the moment.