"János met the girls."

Translation: János a lányokkal találkozott.

[Arcaeca]

What is this -al ending on lányok?

[jsiehler]

The ending for "with" something is -val / -vel. So, in fact, "with something" is valamivel.

However, the v of this ending assimilates with other consonants, causing them to double if they are single. Final a or e become á or é as usual when adding endings. It comes after plural and possessive endings, if there are any. So, some examples:

a folyó + val = a folyóval "with the river"
az alma + val = az almával "with the apple"

az eper + vel = az eperrel "with the strawberry"
az orvos + val = az orvossal "with the doctor"
a lány + val = a lánnyal "with the girl"

a fiúk + val = a fiúkkal "with the boys"
a kezem + vel = a kezemmel "with my hands"

and so on. Besides the "with" meaning, it's also used with certain verbs, and expressions that wouldn't translate as "with" in English. For example, in the lesson about time and seasons you see tavasszal and ősszel for "in spring" and "in autumn".

[Arcaeca]

"with" as in "using" ("with a hammer") or as in "in the company of" ("with his friends")?

Probably the second... so János a lányokkal találkozott literally means "John found himself with the girls"?

[vvsey]

"Talál-koz-ni" means "to meet". The "-koz" suffix makes it... what... maybe reflexive, I don't know. Another word with this suffix is "borotválkozni" - to shave.
"borotválni" - to shave (something/somebody else)
"borotválkozni" - to shave (yourself).

Anyway, "találkozni" is to meet (with people).
Hungarian always uses the "with" way of saying it.

For your sentence,
"John found himself with the girls."
"János a lányok között/társaságában találta magát."

A very similar structure: "found himself" - "találta magát".

[96314081311257]

Találkozik means to meet, but the word does originate from talál (to find.)

-val/vel means with in both meanings. If you want to specify, you need to use more or other words.

Comitative: -val/vel együtt.

Instrumental: there isn't really a standard solution for this, -t használva is a safe bet.

[96314081311257]

One addition I'd like to make is that if a word ends with a silent h, there's no assimilation, of course.

cseh - csehvel

juh - juhval

méh - méhvel

düh - dühvel (or dühhel for some speakers)

but!

sah - sahhal

doh - dohhal

[RyagonIV]

This shatters my image of Hungarian being a language whose rules can be completely decoupled from the actual pronounciation.
Rya szomorú. ;-;

[96314081311257]

Fel a fejjel! :)

This says that there are only nine words ending with a silent h:

céh = guild

cseh = Czech

düh = rage

Enéh (female given name)

juh = sheep

méh = bee

oláh = Romanian (archaic, comes from "vlach", Romanians are super sensitive about it, so don't ever use it)

pléh = tin (plate)

rüh = mange

& there are also names of towns ending with -koh (Vaskoh &c.)

[RyagonIV]

At least there aren't many exceptions, like always. :D
Thanks for that article.

[Pivo302]

The girls are definite. What is the reason to not use Találkozta?

[jsiehler]

The girls are not a direct object marked with the accusative -t ending. So you don't use the definite conjugation. This verb uses the -val/-vel ending for whomever you're meeting, rather than the accusative.