schaffen
to manage
To successfully handle or complete a task or challenge. In this meaning, the verb is conjugated weakly (schaffte, geschafft).
Ich hoffe, ich schaffe die Prüfung morgen.
I hope I manage the exam tomorrow.

to manage / create
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to manage
To successfully handle or complete a task or challenge. In this meaning, the verb is conjugated weakly (schaffte, geschafft).
Ich hoffe, ich schaffe die Prüfung morgen.
I hope I manage the exam tomorrow.

Careful, this verb has two past-tense forms! For 'erfolgreich bewältigen' (to successfully manage; meaning m01), it is weak: schaffte, hat geschafft. For 'etwas Neues erschaffen' (to create something new; meaning m02), it is strong: schuf, hat geschaffen.
Er hat die Prüfung mit Bravour geschafft.
He passed the exam with flying colors.
In the meaning 'etwas bewältigen' (to manage something), 'schaffen' is very often used with the pronoun 'es'. The phrase 'Ich schaffe das!' (I can do it!) is a very typical expression of motivation.
Keine Sorge, wir schaffen das schon zusammen!
Don't worry, we'll manage it together!
In the meaning 'kreieren' (to create), 'schaffen' is often used with abstract nouns. Typical combinations are 'Arbeitsplätze schaffen' (to create jobs), 'Ordnung schaffen' (to create order), 'Klarheit schaffen' (to provide clarity), or 'Platz schaffen' (to make room).
Die neue Fabrik soll 500 Arbeitsplätze schaffen.
The new factory is supposed to create 500 jobs.
When 'schaffen' is used for 'transportieren' (to transport), it often has a slightly colloquial tone. It implies that the transport involves some hurry or effort.
Kannst du die alten Zeitungen bitte in den Keller schaffen?
Could you please take the old newspapers down to the basement?
The fixed expression 'jemandem zu schaffen machen' (to trouble someone / to give someone a hard time) requires the dative. The person having problems is in the dative, while the cause of the problems is the subject of the sentence.
Der Lärm von der Baustelle macht mir zu schaffen.
The noise from the construction site is troubling me.
In southern Germany, Austria, and Switzerland, 'schaffen' is a common word for 'arbeiten' (to work). In other parts of Germany, you would use 'arbeiten' in most contexts.
Was schaffst du denn beruflich?
What do you do for work?
to be able to
'können' and 'schaffen' can both express that someone manages something. 'können' is more general: it is about ability or possibility. 'schaffen' fits better when something is demanding, involves time pressure, or when a goal has to be reached. Learners confuse the words because you can often ask either 'Kannst du das?' (Can you do that?) or 'Schaffst du das?' (Can you manage that?). The difference is the perspective: 'können' asks about the possibility or ability, while 'schaffen' asks about successfully getting it done.

Wir schaffen die Vorbereitung heute noch, wenn alle mithelfen.
We will still manage the preparations today if everyone helps.
Wegen des Streiks kann Lisa am Montag nicht nach München fahren.
Because of the strike, Lisa cannot travel to Munich on Monday.