
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.

to facilitate
To mediate in a conflict, meeting, or workshop in order to find a solution or make the process easier.
Ein externer Berater wurde engagiert, um den schwierigen Workshop zu moderieren.
An external consultant was hired to facilitate the difficult workshop.

to moderate
In an online forum or community, to monitor users' posts, remove inappropriate content, and ensure that the rules are followed.
Er moderiert ehrenamtlich ein großes Forum für Computerspiele.
He volunteers as a moderator for a large computer games forum.
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
Both words can occur in connection with a television or radio show, but they refer to different tasks. Someone who introduces content or results präsentiert them; someone who leads the entire show and guides the audience through its individual segments moderiert it. So pay attention to whether the focus is on the content or on the program's flow.

Im Abendprogramm moderierte der Journalist die gesamte Sendung.
During the evening program, the journalist hosted the entire show.
Im Abendprogramm präsentierte die Expertin die Ergebnisse der neuen Umfrage.
During the evening program, the expert presented the results of the new survey.