Be fast and be prepared.
If you find an apartment online that you really want, try to get the earliest appointment you can get. Try even the same day. The market is incredible fast at the moment. Seeing a flat on the 25th and moving in on the 1st is not uncommon.
Bring everything with you to the first visit that you could imagine that brings you into a good light to the landlord. A CV, a short letter about yourself, documents about your salary etc.
Decide on the spot if you take it or not.
Do a follow up call the next day, to show your real interest. Be nice. Good luck.