In English we can 'feel' like doing things. We can also 'feel' a certain way. For example, we can feel like swimming, cooking, sleeping, playing a game or a sport, or whatever. We can also 'feel' emotional about something, like feeling happy, sad, lucky, sorry, embarrassed, or depressed maybe. And we can 'feel' a certain way physically, like feeling good, sick, tired, strong, etc. The English verb "to feel" is very versatile and used broadly.
How one expresses feelings in Spanish depends on what those feelings are. In other words, not just one verb is used to indicate someone is feeling something.
In Spanish, generally, expressing a desire to do something or some activity, one uses the phrase "tenerganas de", followed by a infinitive verb describing what the activity is. The verb tener (to have) is conjugated to whoever is feeling like doing something, followed by 'ganas', which means desire, then 'de', and then the infinitive verb to describe what it is. Look at these examples:
I feel like swimming. - Tengoganas de nadar.
Do you feel like eating? - ¿Tiene(s) ganas de comer?
I feel like playing golf today. - Tengoganas de jugar golf hoy.
Do you feel like exercising this morning? - ¿Tiene(s) ganas de hacerejercicioestamañana?
If you can conjugate tener, and follow it by 'ganas de', the only thing left is the infinitive verb indicating what is desired.
If you want to ask someone what they feel like doing, it is a little different, but not by much:
What do you feel like (doing)? - ¿De quetiene(s) ganas?
What do you all feel like doing? - ¿De quetienenganas?
If someone asks you what you feel like doing, you respond with the "de" first:
Fred. What do you feel like doing? - Señor Fred. ¿De quetienesganas?
I could reply, always starting with the "de":
"Nothing". - De nada.
Or, "playing golf". - De jugar golf.
Now let's look at how we express emotions or physical feelings in Spanish. The reflexive form of the verb Sentir (sentirse), 'to feel', is most often used. If you need some review on reflexive verbs, you might like to review the article "How Are Your Spanish Reflexes?"
Let's look at some uses of sentir(se) expressing feelings of emotion, physical or emotional states:
How do you feel? - ¿Cómo se siente? or ¿Cómotesientes? - informal.
I feel fine (well). - Me sientobien.
I feel sick. - Me sientoenfermo.
We are (feel) embarrassed. - Nos sentimosavergonzados.
She feels bad about that. - Se siente mal sobreeso.
I hope you feel better. - Esperoque se sientamejor. (Do you recognize the subjunctive)?
Now take a look at probably the most common use of sentir. You probably are already familiar with it.
I'm sorry. - Lo siento.
"Lo" here is a Spanish direct object pronoun meaning 'it'.
And 'siento' is the 'yo', (I), conjugated form of sentir. This literally translates to "it, I feel". Notice sentir is not used reflexively here (no reflexive pronoun).
And to say what you are sorry for, you follow 'lo siento' with 'por' and an infinitive verb describing what it is that you are sorry for:
I am sorry for arriving late. - Lo sientoporllegartarde.
There are other ways to express feelings of desire, emotion, physical states etc. in Spanish. Most are variations of the above. But these above methods are probably the most common. If you become familiar with just these, you will be able to say what or how you feel and ask someone the same. It is very handy to know how to do this in Spanish.
As always, find opportunity to practice using 'tenerganas de' and 'sentirse' (and all the Spanish you have learned so far) in real real- time. Spanish theory is helpful and good to know, but it's not about theory. It's all about speaking, understanding, and how you 'feel' about Spanish. Remember to have fun with it!