You have a few options:
1. Apply for a
spouse visa under the UK immigration rules. This visa is costly and has maintenance and English language requirements but will allow your wife to apply for British citizenship after 3 years in the UK.
2. Apply for a
EEA Family Permit. This application is free and the requirements are much easier to meet if you worked in the EU. However, the path to British citizenship will take 5 years.
If you don't want to apply for a visa at all, the best option would be to drive to Calais, France and seek entry at the port. This way you don't need to deal with airlines which will not allow your wife to fly to the UK without a visa. At the port, you will need to provide the same evidence needed for EEA Family Permit, namely a marriage certificate and proof you have been working in Germany. See more
Can family members of British citizens qualify for an EEA family permit? ('Surinder Singh' cases).