Comparing

"More" is יוֹתֵר yoter, before or after the adjective, and "than" is the prefix מִ or מֵ, "from" (One-letter words). Hebrew has no special forms like "better" or "biggest": "better" is טוֹב יוֹתֵר tov yoter.

• דָּנִי גָּבוֹהַּ יוֹתֵר מִדָּנָה.
  dani gavo'ah yoter midana
  Dani is taller than Dana.
• הַבַּיִת הַזֶּה יוֹתֵר גָּדוֹל.
  habayit haze yoter gadol
  This house is bigger.
• תֵּל אָבִיב יְקָרָה יוֹתֵר מֵחֵיפָה.
  tel aviv yekara yoter mekheifa
  Tel Aviv is more expensive than Haifa.

"Less" is פָּחוֹת pakhot, used the same way, and "much more" is הַרְבֵּה יוֹתֵר harbe yoter.

Than me

Before a pronoun, "than" is מִן with an ending (Prepositions with endings): מִמֶּנִּי mimeni "than me", מִמְּךָ mimkha and מִמֵּךְ mimekh "than you", מִמֶּנּוּ mimenu "than him", מִמֶּנָּה mimena "than her", מֵהֶם mehem "than them".

• הִיא צְעִירָה מִמֶּנִּי.
  hi tse'ira mimeni
  She's younger than me.

The most

הֲכִי hakhi before an adjective is "the most": הֲכִי טוֹב "the best". With a noun, the noun takes ה and the adjective doesn't. Formal Hebrew puts בְּיוֹתֵר beyoter after an adjective with ה instead.

• זֶה הַסֶּרֶט הֲכִי טוֹב שֶׁרָאִיתִי.
  ze haseret hakhi tov shera'iti
  It's the best film I've seen.
• מָה הָעִיר הַגְּדוֹלָה בְּיוֹתֵר בְּיִשְׂרָאֵל?
  ma ha'ir hagdola beyoter beyisra'el?
  What's the biggest city in Israel?
  formal

As … as, and the same

כְּמוֹ kmo "like, as" says two are alike: גָּבוֹהַּ כְּמוֹ "as tall as". "The same" is אוֹתוֹ oto, אוֹתָהּ ota or אוֹתָם otam before the noun, agreeing with it, and "different from" is שׁוֹנֶה מִ shone mi-.

• הוּא גָּבוֹהַּ כְּמוֹ אַבָּא שֶׁלּוֹ.
  hu gavo'ah kmo aba shelo
  He's as tall as his father.
• אֲנַחְנוּ גָּרִים בְּאוֹתוֹ רְחוֹב.
  anakhnu garim be'oto rekhov
  We live on the same street.
• זֶה אוֹתוֹ דָּבָר.
  ze oto davar
  It's the same thing.