An investment philosophy is a set of rules or guidelines that you abide to help you navigate through treacherous markets. Just as in life, most of us have moral principles that we abide, for e.g. we do not steal or commit adultery but tell our wives we are working when we go to pubs, we value life and are fillial to our parents, we feed monkeys that come to us with bananas and are loyal to friends etc. In investment, you must also lay down the rules, and learn not to break them. Collectively, this set of rules and principles will be known as your investment philosophy and will serve you well in time to come.
An investment process is the execution. It will determine how you start looking for stock ideas, when to buy them, when to sell, what are the maintenance research that you have to do etc.
The investment philosophy that I subscribe to, is similar to that of the world's greatest investor. I look for
1) Stocks that are cheap, i.e. trading below intrinsic value
2) Margin of Safety: chances of losing money are minimized
3) Stocks that pay dividends
The investment process that I subscribe to, though not similar to the guru, hopefully make sense to most people and not so much to monkeys
1) Observations in daily life to come up with stock ideas
2) Wait for a good time to buy (i.e when the stock falls)
3) Know when to exit in both cases where a) things go as expected, b) things did not go as expected
Investment philosophy and process evolves over time and is different for everyone. A day trader will have another set of guidelines and process, but the most important rule is never to deviate from your own philosophy. In life, to stray away may give you temporary satisfaction, but never the peace of mind. In investment, to stray away may give you temporary rewards, but will not help you make money over the long run.
See also Three Principles of Value Investing