This is the shape of the process rather than a substitute for it. Requirements differ between German missions, and the mission covering your country is the only authority on what it wants. Check its own page before you act on anything here.
Start with the appointment, not the paperwork
At many missions the appointment is the bottleneck. Waiting times can run to months, and they are worst in exactly the season everyone is applying.
Book as soon as you have an admission letter — earlier if the mission allows it. You can assemble documents while you wait. You cannot manufacture an appointment slot once the semester is close.
Proof of finances
Germany requires evidence that you can support yourself for the first year. Most students meet this with a blocked account: money deposited with an approved provider and released to you in monthly instalments once you arrive.
The required amount is set by the authorities and changes. Look it up on the mission's page rather than relying on a figure from a forum post — this is the number people most often get wrong, and being short means a refusal.
A scholarship award letter can substitute where the scholarship covers living costs. Check whether yours qualifies before opening a blocked account you may not need.
Health insurance
You need cover from the day you arrive. Travel insurance covers the gap before enrolment; German statutory student insurance takes over once you are enrolled. Many students arrange the statutory policy before travelling and carry the confirmation to the visa appointment.
At the appointment
Bring the originals and a set of copies. Bring more copies than the checklist says. Missions differ on what they keep.
Expect questions about why this course, why Germany, and what you intend to do afterwards. These are not trick questions, but a vague answer is a problem. Be able to name your university, your programme and your reason for choosing it.
After you arrive
Register your address, open a bank account, enrol, and apply for your residence permit before the visa expires. The registration usually has to come first because everything else asks for it.
Most delays at this stage come from appointment availability at the local registration office, which is the same problem as at the start. Book early.