No part of the word is conjugated in any person. 

No part of the word or its conjugation means/shows "you" as the object.

Korean verbs are not conjugated as they are in English, German, Spanish, Italian, Portuguese, French, etc. They are not conjugated differently based on the subject. 

I eat, you eat, he eats, she eats, it eats, we eat, you all eat, and they eat are all the exact same thing in Korean (in 요 form): 먹어요

Versus Spanish -> yo como, tú comes, él come, ella come, Usted come, nosotros comemos, vosotros coméis, ellos comen, ellas comen, Ustedes comen

In those languages where verbs are conjugated based on person, the subjects can be omitted because the verb ending denotes the subject. This is not the same as Korean and Japanese, since their verb endings do not showing who is performing an action or is a certain way.

Korean (as well as Japanese) often omit the subject or other words/particles if they're easily understood within the context of the situation. It's also based on their culture of being very humble, polite, and respectful. It's rude and weird to keep saying I, I, I, I, I, I.

사랑해요 literally just means "love(s)" (as a verb).

<em>It does not tell you who is doing the loving or who is being loved.</em>

<em></em>However, if you were to say this to someone, it would be understood as "I love you" since you ("I") are the one speaking and he or she ("you") is the one being spoken to.

If you want to literally say "I love you" it would be (there are different variations of course, I used particles to demonstrate):  난 널 사랑해.

It is not the conjugations of words that denote subjects and objects, it's particles. That's their whole purpose - to show the role of a word in a sentence.

In Spanish and Portuguese, the ending gives you a pretty good idea of the subject and words like "me" and "te" show the object. In Korean, the particles tells you! 은/는 - who it's about (versus -o, -as/es, -a/e, etc); 이/가 - who is; 을/를 - what/who is the object!

Let me know if you have any more questions.

Likewise, nouns don't change either based on whether they are the subject or direct object or indirect object, etc.

저/나 - could mean "I" or "me" (so unlike in English, it doesn't change forms, from I to me)

제/내 - could mean "my" or "mine" (again doesn't change forms, from my to mine)

"to me" would be conveyed using the same form of "I" (저/나) and a grammar particle. (Vs. Spanish: yo -> me; ex. "dime")

사랑해

사랑해요

(사랑하세요)

사랑합니다

(사랑하십니다)

These all mean the exact same thing (except the ones in parenthesis cannot mean "I", as they are honorific and you can't talk about yourself in that way because that's extremely conceited, narcissistic, and rude): Any of the following, based on context or the actual inclusion of a subject

I love, you love, he loves, she loves, it loves, we love, you all love, they love

It also doesn't matter about number.

"The dog is fat" 개가 뚱뚱해요.

"The dogs are fat" 개가 뚱뚱해요. (Koreans don't usually use the plural particle [for nouns only][again based on context and so omitted]. But if you needed to emphasize this fact it would be 개들이 뚱뚱해요)

사랑하다 - to love (action verb)

사랑 - love (noun)

하다 - to do (action verb)

Conjugating 사랑하다 in the simple present tense (반말 & 요 form)

사랑하다 -> 사랑하 -> 사랑하+여(요) -> 사랑하여(요) -> 사랑해(요)

Korean uses grammar instead of words to express meaning. So there's a gazillion different endings depending on what you mean. Some grammar structures can only be used with certain subjects. So you could say these endings show subject or listener through process of elimination and context. But you never conjugate according to number or person.