sprechen
to speak
To have and use the ability to articulate sounds, words, and sentences; to talk.
Nach dem Schock konnte er eine Weile nicht sprechen.
After the shock, he couldn't speak for a while.

to speak
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to speak
To have and use the ability to articulate sounds, words, and sentences; to talk.
Nach dem Schock konnte er eine Weile nicht sprechen.
After the shock, he couldn't speak for a while.

The verb 'sprechen' (to speak) is the root of many important words related to communication. These include 'die Sprache' (the language; the system one speaks) and 'der Spruch' (a short, often wise saying).
Welche Sprachen sprichst du?
Which languages do you speak?
The meaning of 'sprechen' (to speak) changes depending on the preposition. You speak 'mit' (with) a person (dative), but 'über' (about) a topic (accusative).
Ich spreche mit meinem Freund.
I speak with my friend.
The perfect tense of 'sprechen' (to speak) is always formed with the auxiliary verb 'haben' (to have). The past participle is 'gesprochen' (spoken).
Wir haben lange über die Zukunft gesprochen.
We spoke for a long time about the future.
When talking about languages, 'sprechen' (to speak) is often combined with adverbs that describe the level. Typical examples are 'fließend sprechen' (to speak fluently), 'gut sprechen' (to speak well), or 'ein bisschen sprechen' (to speak a little).
Er spricht fließend Spanisch.
He speaks Spanish fluently.
The expression 'für sich sprechen' (to speak for itself) is often used for things that are so clear that they need no comment. Typical subjects are 'die Zahlen' (the figures/numbers), 'die Ergebnisse' (the results), or 'die Fakten' (the facts).
Die Ergebnisse der Studie sprechen für sich.
The results of the study speak for themselves.
In the expression 'gut/schlecht auf jemanden zu sprechen sein' (to think well/poorly of someone), the person being referred to is always in the accusative after the preposition 'auf'.
Nach dem Streit ist er nicht gut auf seinen Nachbarn zu sprechen.
After the argument, he doesn't think well of his neighbor.
The combination 'ein Urteil sprechen' (to deliver a verdict) belongs to the formal language of the justice system. This phrasing is not used in everyday speech.
Der Richter wird morgen das Urteil sprechen.
The judge will deliver the verdict tomorrow.
to be able to
'können' and 'sprechen' overlap especially when talking about languages. You can say: 'Ich kann Deutsch' (I know German / I can speak German) or 'Ich spreche Deutsch' (I speak German). 'können' emphasizes the ability or mastery of the language. 'sprechen' emphasizes that you use the language and can communicate in it. The words can be confusing because both sound natural with languages. When you are talking generally about a learned ability, 'können' works well. When the focus is communication in a language, 'sprechen' sounds more precise.

Am Wochenende hat sie mit den Gästen Spanisch gesprochen.
At the weekend, she spoke Spanish with the guests.
Nach dem Kurs kann Mehmet einfache Gespräche auf Deutsch führen.
After the course, Mehmet can have simple conversations in German.