It may be useful to learn words in related “families,” so let us look at several verbs that share their root with дава́ть [dɐˈvatʲ], to give. I will include the imperfective and perfective forms of the verb and any related nouns for each verb. This post does not cover every verb or every possible meaning. Feel free to add to the list in the comments. I will be using the International Phonetic Alphabet for transcriptions.

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Давать

The basic verb means “to give” and has the following forms:

• дава́ть [dɐˈvatʲ], imperfective
  
• дать [datʲ], perfective.

Отдавать

To give away; to give back

• отдава́ть [ɐdːɐˈvatʲ], imperf.
• отда́ть [ɐˈdːatʲ], perf.

Задавать

This verb can mean “to assign” but can also go together with such words as вопро́с [vɐˈpros], “question,” to form задавать вопрос, “to ask a question.”

• задава́ть [zədɐˈvatʲ], imperf.
• зада́ть [zəˈdatʲ], perf.
• зада́ние [zɐˈdanʲɪje], noun: assignment, homework

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Продавать

To sell

• продава́ть [prədɐˈvatʲ], imperf.
• прода́ть [prəˈdatʲ], perf.
• прода́жа [prɐˈdaʐə], noun: sale

Сдавать

This verb has several meanings. It can mean “to give something away,” as in your position or information. It can also mean to rent something to someone. Finally, combined with экза́мен [ɪɡˈzamʲɪn] it сдавать means to take an exam, and сдать to pass an exam—the perfective here signals successful completion.

• сдава́ть [zdɐˈvatʲ], imperf.
• сдать [zˈdatʲ], perf.
• сда́ча [ˈzdat͡ɕə], noun: change (from a sum of money)

Передавать

to transfer; to transmit; to pass along (a message)

• передава́ть [pʲɪrʲɪdɐˈvatʲ], imperf.
• переда́ть [pʲɪrʲɪˈdatʲ], perf.
• переда́ча [pʲɪrʲɪˈdat͡ɕə], noun: a TV or radio show

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Издавать

This verb can mean “to publish” (in print) or “to issue” (a decree or law).

• издава́ть [ɪzdɐˈvatʲ], imperf.
• изда́ть [ɪzˈdatʲ], perf.
• изда́ние [ɪzˈdanʲɪje], noun: edition
• изда́тельство [ɪzˈdatʲɪlʲstvə], noun: publishing house

Предавать

This verbs primarily means “to betray,” but it can also mean “to subject to something,” like “преда́ть огла́ске,” “to make public.”

• предава́ть [prʲɪdɐˈvatʲ], imperf.
• преда́ть [prʲɪˈdatʲ], perf.
• преда́тельство [prʲɪˈdatʲɪlʲstvə], noun: treason

What would you add to this list?