arbeiten
to work
To have paid employment in order to earn a living; to be employed.
Sie arbeitet als Ärztin in einem großen Krankenhaus.
She works as a doctor in a large hospital.

to work
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to work
To have paid employment in order to earn a living; to be employed.
Sie arbeitet als Ärztin in einem großen Krankenhaus.
She works as a doctor in a large hospital.

The verb 'arbeiten' (to work) belongs to a large word family. Important related words are the noun 'die Arbeit' (work) and the adjective 'arbeitslos' (unemployed).
Er hat viel Arbeit in dieses Projekt investiert.
He invested a lot of work in this project.
To name a profession, you use the structure 'arbeiten als' (to work as) + job title in the nominative. This is a very common and useful construction.
Mein Bruder arbeitet als Programmierer in Berlin.
My brother works as a programmer in Berlin.
To name the employer or company you work for, you use the preposition 'bei' followed by the dative.
Ich arbeite bei einer großen deutschen Firma.
I work for a large German company.
When you are working on a project, task, or problem, you use the fixed preposition 'an' with the dative: 'an etwas arbeiten' (to work on something).
Die Wissenschaftler arbeiten an einem neuen Medikament.
The scientists are working on a new medication.
When the subject of the sentence is a machine, device, or system, 'arbeiten' (to work) means something like 'funktionieren' (to function) or 'in Betrieb sein' (to be in operation).
Meine alte Kaffeemaschine arbeitet nicht mehr richtig.
My old coffee machine doesn't work properly anymore.
In connection with dough, wine, or wood, 'arbeiten' (to work) means that a material is changing through internal, natural processes.
Das Holz des neuen Tisches arbeitet und zieht sich bei Kälte zusammen.
The wood of the new table is working and contracts in the cold.
to do / make
'machen' and 'arbeiten' both have to do with activity. 'machen' is very general and can refer to almost any action. 'arbeiten' is used when an activity involves effort, work, or a specific project. So you can say 'Hausaufgaben machen' (to do homework), but if you spend a long time concentrating on it, you can also say 'an den Hausaufgaben arbeiten' (to work on the homework). Learners confuse the words because both express activity. 'arbeiten' is more specific when it is about effort, a job, or spending a longer time on something.

Für die Prüfung arbeitet Lisa jeden Abend eine Stunde.
Lisa works for an hour every evening for the exam.
Frau Kaya macht für ihre Klasse neue Übungen.
Ms. Kaya makes new exercises for her class.