"Holnap felhívlak"
"Majd eszem"

"Fog" is the verb you can use to make future tense in the same way you do it in English with "will". But if you have already some adverbs marking the future (as you actually have) you can also use present tense.
This is my answer as a learner, please don't rely too much on it. :-/

Hi Julia! We mainly use "fog csinálni valamit" ("will do something"), or "lesz" ("will be") to express future tense, but we also use the form similar to the "Present Continuous for Future" tense in English, which is more common.

-->

Holnap fel foglak hívni. = I'll call you tomorrow. - correct, but not used too often --> Holnap felhívlak. - more common form

Fel fogom hívni. = I'll call him. - it's much more common if we don't specify the exact time

Később fogok enni. / Később eszem. = I will eat later. - the emphasis is on the fact that the action will happen at a later time

Majd eszem. = I will eat at some point of the day.

Az előadás holnap lesz. = The performance takes place tomorrow.

Délután a városban leszek. = In the afternoon I'll be in the city.

It's more common to omit "fog" when talking in the future tense.

Holnap megyek vásárolni. (rather than "fogok menni") = I'm going shopping tomorrow.

Reggel hazautazom. (rather than "haza fogok utazni) = In the morning I'm travelling home.

Hope this helps.

Не за что! :-)

In spite of Hungarians seem to prefer the form with adverb, anyhow you can use the verb "fog" (conjugated) with the infinitive:
"Fogok menni" (I'll go)
"Fogok enni" (I'll eat)
"Fogok főzni" (I'll cook)

Take care that the verb "fog" take the indefinte/definite conjugation depending the main verb:
"A gulyast fogom enni" (I'll eat the gulash)
"A pörköltöt fogom főzni" (I'll cook the stew)

... and if the main verb has a prefix, they are splitted:
"Kimegyek" (I go out)
"Ki fogok menni" (I'll go out)

Always wait for a native's (or more skilled one's) opinion! :-ʃ

Thank you! And what if i don't have such adverbs? for example - I will go, I will eat, I will cook?