What are good methods to keep you hair strong and keep from falling out?

Healthy diet, proper care. But many factors including heredity, over all health and age often are factors you can not do anything about. Some men go bald by 30. Others have full hair at 60

Do not use an anti dandruff shampoo on a regular basis, especially the over the counter ones as these can lead to hair damage.
Do not keep artificial colours in your hair all through the year, once it runs out let your hair be the colour it is, at least for a period of 2-3 months before you go for that streaking/global colouring treatment again.
Do not get multiple treatments like colouring and straightening at/around same time. Give your hair some rest.
Do not comb wet hair rigorously. Patience is the key for healthy tresses and also wet hair will shed more, so avoid combing them again and again.
Do not indulge in too many hair packs like vinegar and eggs, etc in one go. Overdoing hair packs can cause severe alterations in hair health.
Do not over-use hair styling gels. Stay away from chemical-heavy hair straightening gels and lotions that promise 'soft' hair with just one dab of ointment.
Avoid over-use of hair sunscreens, but conditioners can fulfill this task quite well.
Use a wide toothed comb if hair fall is present. Please do not use a combing brush or small comb. Also, avoid sharing your comb with others especially when you do not know their scalp coniditon.
If you have scalp psoriasis and also dandruff then do not oil your hair. As oil is like a meal for malasezia yeast that is the causative organism for dandruff.
Do not tie your tresses in a bun all the time, if you have long hair. This can lead to traction alopecia and lead to hairfall as well.