suchen
to look for
To try to find someone or something that you have lost or whose location you do not know.
Ich suche meinen Schlüssel, hast du ihn gesehen?
I'm looking for my key; have you seen it?

to search / look for
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to look for
To try to find someone or something that you have lost or whose location you do not know.
Ich suche meinen Schlüssel, hast du ihn gesehen?
I'm looking for my key; have you seen it?

The verb 'suchen' (to search/look for) is the stem for other important verbs such as 'versuchen' (to try something), 'besuchen' (to visit someone), and 'untersuchen' (to examine something closely).
Ich versuche, Deutsch zu lernen.
I am trying to learn German.
'Suchen' (to search/look for) is usually used with an accusative object when you are looking for a concrete thing or person. The preposition 'nach' (+ dative) is used when the search is more intensive or the goal is more abstract.
Ich suche mein Handy.
I'm looking for my phone.
When 'suchen' (to look for) is used with objects like 'eine Wohnung' (an apartment), 'einen Job' (a job), 'Arbeit' (work), or 'das Glück' (happiness), it does not mean that something is lost, but that you are trying to find something new for your life.
Meine Schwester sucht eine neue Arbeitsstelle in Berlin.
My sister is looking for a new job in Berlin.
The construction 'suchen nach' (to search for) is often used for abstract things. Typical combinations are: 'nach einer Lösung suchen' (to search for a solution), 'nach einer Antwort suchen' (to search for an answer), or 'nach dem Sinn suchen' (to search for meaning).
Die Ingenieure suchen nach einer Lösung für das technische Problem.
The engineers are searching for a solution to the technical problem.
The expression 'hier nichts zu suchen haben' (to have no business being here) is a fixed phrase. It strongly expresses that someone is unwanted in a place or should not be there.
Du hast hinter der Bar nichts zu suchen!
You have no business being behind the bar!
to find
'suchen' and 'finden' often belong to the same situation, but they show two different steps. 'suchen' means that you are trying to get or discover something because you do not have it yet or do not know where it is. 'finden' means that you discover it in the end or by chance. You can search for a long time and find nothing. With abstract things, it is similar: you search for an answer and may find a solution. Learners easily confuse the words because they often occur together. A practical tip: 'suchen' is the attempt; 'finden' is the result.

Die Fahrerin sucht morgen eine Werkstatt in der Nähe.
Tomorrow the driver is looking for a garage nearby.
Nach zehn Minuten finde ich meinen Schlüssel unter dem Sofa.
After ten minutes, I find my key under the sofa.