Well, after searching inside for an hour and then deciding to try looking outside, it should be pretty clear what you're looking for. :)
You might also say "I'm looking for it outside" to state that there's something you're looking for. That would require the definite conjugation and look like this: "(Én) kint keresem."
But of course. :)
Hungarian has two modes of conjugation that most other languages don't have. They are commonly called "indefinite" and "definite" conjugation. The main difference is that the definite conjugation refers to a definite direct object, while the indefinite mode is used whenever there is no object to refer to, or it's a more general object. Some examples:
- A pillangót látom. - I see the butterfly. Definite conjugation because the butterfly is a certain one, indicated by the article a.
- Pillangót látok. - I see a butterfly. Indefinite conjugation, because it's just some random insect.
- Látok. - I can see. Indefinite conjugation. There is no object to see, I just state my ability.
And here's the trick: if you use the definite conjugation without naming an object, the object is assumed. This is expressed most often with "it" as a dummy object in English, but can refer to anything* you've spoken about before.
- Látom. - I see it (or him, her, them). This sentence can also be used where you would say "I see" in English after someone has explained something to you. The assumed object here would be the explanation given to you.
Now, as you've learned, Hungarian has a distinct suffix for each conjugational form. That's why you can leave out the pronouns of the sentences. The same accounts for the definite conjugation. Let's stick with lát for a bit, as our back-vowel example:
- én látok - látom
- te látsz - látod
- ő lát - látja
- mi látunk - látjuk
- ti láttok - látjatok
- ők látnak - látják
- én látlak téged; this last form is the wonderfully short I-you form that's probably unique to Hungarian. It's always used if the subject is I (én) and the direct object is you (singular or plural; téged or titeket). Látlak means "I see you."
For high-vowel verbs let's try again with keres, even though the sibilant makes is a bit irregular.
- én keresek - keresem
- te keresel - keresed (the indefinite form usually takes -sz, but if the last consonant is a sibilant, it defaults to -ol/-el/-öl)
- ő keres - keresi
- mi keresünk - keressük (the definite suffix would be -jük, but the j gets assimilated after sibilants)
- ti kerestek - keresitek
- ők keresnek - keresik
- én kereslek téged
And because I'm a completionist, another round for verbs with rounded high vowels (ö, ő, ü, ű). Example is tör - to break
- én török - töröm
- te törsz - töröd
- ő tör - töri
- mi törünk - törjük (there you have the proper -jük)
- ti törtök - töritek
- ők törnek - törik
- én törlek téged
(As you can see, it diverts from the normal high-vowel conjugation just in four forms: in the indefinite conjugation in 1st ps. sing. (én) and 2nd ps. plur. (ti), and in the definite one in 1st and 2nd ps. sing. (én and te))
That's a lot to take in, I admit. You'll learn properly about definite conjugation in later sections, but this is a brief outline of this (quite fascinating) matter. Hungarian has a steep entry for learners, unfortunately. But now you can see where the -em suffix in keresem comes from. It tells me that it's definite conjugation and that you're looking for something certain (or someone certain, or even multiple certain things or people).
And now for the magical asterisk up there. :D
* It's not technically anything you've spoken about, but only accounts for objects that are grammatical third persons: him, her, it, them. And any name or named object.
If the direct object, however, is either me, you, or us, the indefinite form gets used. Kinda weird, but that's how it is:
- Téged keres. - He is looking for you.
- De te minket szeretsz. - But you love us.
- Látsz engem? - Do you see me?
Or, as I established earlier, with the I-you form:
- Szeretlek. - I love you.
- Titeket látlak. - I see you (all).
That's why I said that this form is fantastically short. The -lak/-lek suffix literally makes a verb into "I [verb] you."
- Kint látlak. - I see you outside.
- Zavarlak? - Do I disturb you?
- Akarlak csókolni. - I want to kiss you.
- Szeretlek. - I love you. (Probably the most famous Hungarian sentence.)
Of course you can always add the object téged or titeket (you and plural you, respectively) for clarity. But it's not needed. Just like mentioning of the object is not needed when you use the definite conjugation.