Titanium is virtually eternally durable and doesn't really require special care, but like all jewelry, it will scratch and develop its own patina, although at a much slower rate than softer metals like silver or gold.
Our first recommendation is always to wear your jewelry as you see fit, and let it live with you, titanium is tough. Yet you might want to restore its original look, or manually clean it once in a while. Taking care of titanium is very easy though.
How to clean Titanium Jewelry
Put your titanium jewelry in a bowl of water and mild soap for a few minutes. Then remove the jewelry and gently brush the surfaces with a soft cloth.
You can also use an ultrasonic cleaner found in jewelry stores. Taking a shower with your jewelry will also naturally clean it.
How to remove scratches
If you wish to remove scratches from your titanium jewelry, you can use either a nylon pad (scotch brite for instance) or a cream metal polish, and rub it with a soft cloth.
Rinse with water after you're done and the jewelry should be like new.