What suggestions can you give to keep tea from staining my teeth?

Stained plaque=stain. Most extrinsic (surface level) stain is essentially plaque that has been dyed by coffee tea cola etc. Incomplete removal of this soft stained plaque, from lack of correct daily flossing and/or appropriate vibratory toothbrushing techniques focusing at the gum tooth interface , results in soft plaque absorbing salivary calcium to harden on the tooth surface (calculus) requiring a dental cleaning.
Don't drink tea. Tea will stain (cosmetic stain, not a scar) teeth, but your dentist can remove tea stain. You can rinse with plain water immediately after drinking tea to wash away the stain producing pigments. I would not brush immediately after drinking tea because tea is acidic, and that temporarily weakens the enamel. Also consider a whitening toothpaste.
Brush right after. Tea and coffee tend to stain teeth fairly quickly. The only way to limit this is to brush and floss as soon as possible after having that cup of tea. I find electric toothbrushes seem to do a better job for many patients than a hand tooth brush. Try it and see if it helps. Also, see a dentist for professional cleanings as necessary.