The definite article
הַ plus a following dagesh is the basic "the." Vowels under ה change before gutturals.
The default
הַ with patah, and dagesh in the next letter when that letter can take it: הַמֶּלֶךְ, הַיּוֹם. Prefix prepositions בְּ לְ כְּ swallow the ה and keep its vowel: בַּיּוֹם.
the king
the day; today
on the day
Before gutturals
Aleph, he, het, ayin (and often resh) reject dagesh. The article lengthens or lowers: הָאָרֶץ, הֶהָרִים. Learn a few high-frequency shapes rather than memorizing every rule first.
the earth, the land
the man
the mountains
Names and construct
Personal names are already definite. A construct chain takes the article only on the last member, never on the construct noun itself.
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Construct chains
Smikhut: two (or more) nouns in a row, the first in construct, the last carrying definiteness for the chain.
The direct object marker
אֵת (often אֶת) flags a definite direct object. It has no English word of its own.
Biblical prepositions
A closed set of short words does the work of English "in, to, from, on, before, after."