Iiquid detergent is a good way I've known to wash any glasses. It works well and doesn't harm the glasses. Put a few drops of liquid detergent in the clean water, then put your glasses in it and wash them. Finally rinse under the clean, running water.
Anyway, the basic ways of cleaning are just the same with other glasses. However, there you should pay more attention because titanium frames are afraid of something acid, therefore, just try not to use a lot of detergent for cleaning. Just try to use warm water and a piece and soft cloth.
There is a kind of solution that can help clean your frame. You can consult an optician in any optical shops. Sometimes the optician will give away a bottle of free solution if it is the first time you buy glasses from their store.
I have a pair of titanium glasses. I think you don't need to buy special solution to clean them. Titanium is resistant to corrosion. If you clean them with a piece of glass cloth before you put them into a case. They will be fine. You just need to wash the cloth regularly. Or you can rinse your glasses with mild cleaner and then dry them with clean soft towel.
You can use dishwashing soap to clean your glasses. Rinse the lenses in a circular motion and wash the frame gently. Then you can rinse the lenses and frame with tap water. Some people may dip the glasses in the soap water. But that is not a good way to clean the frame. You'd better rinse them rightly after you washed them carefully. Good luck!