moderieren
to host
To lead an event, a television or radio show, or a panel discussion and guide the audience through the program.
Sie moderiert eine bekannte Talkshow im Fernsehen.
She hosts a well-known talk show on television.

to host / moderate
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to host
To lead an event, a television or radio show, or a panel discussion and guide the audience through the program.
Sie moderiert eine bekannte Talkshow im Fernsehen.
She hosts a well-known talk show on television.

Verbs that end in '-ieren' form the past participle without 'ge-'. So it is 'hat moderiert' (has hosted/moderated) and not 'hat gemoderiert'. This is an important rule for many verbs borrowed from other languages.
Er hat die Diskussion sehr professionell moderiert.
He moderated the discussion very professionally.
The object of the verb makes the meaning clear. 'Eine Sendung moderieren' (to host a show) refers to media, 'einen Workshop moderieren' (to facilitate a workshop) refers to leading a group, and 'ein Forum moderieren' (to moderate a forum) refers to controlling online content.
Wer wird die politische Debatte im Fernsehen moderieren?
Who will host the political debate on television?
'Moderieren' does not mean to make something less extreme or less intense, like the English 'to moderate' (e.g. one's views). For that, German usually uses the verb 'mäßigen' (to moderate/temper).
Der Politiker wurde gebeten, seine scharfe Kritik zu mäßigen.
The politician was asked to moderate his harsh criticism.
In the media world, people typically 'moderiert' (host) 'eine Sendung' (a show), 'eine Talkshow' (a talk show), 'eine Gala' (a gala), or 'eine Podiumsdiskussion' (a panel discussion).
Nächstes Jahr darf sie die große Preisverleihung moderieren.
Next year she will be allowed to host the big awards ceremony.
to present
'präsentieren' and 'moderieren' both often occur at events, broadcasts, or meetings. 'Präsentieren' means that you present content, a product, or a result. 'Moderieren' means that you host a program, lead discussions, or organize the order of contributions. Learners may confuse the words because one person on stage sometimes does both. Put simply: someone who 'präsentiert' shows or explains something. Someone who 'moderiert' guides others through the event.

Timo moderiert am Morgen die Diskussion im Radio.
Timo hosts the discussion on the radio in the morning.
Der Chef präsentiert beim Termin die neuen Zahlen.
The boss presents the new figures at the meeting.