An investment strategy is an approach to choosing investments. This can also be called an investment style. Different investment strategies reflect investors' varying objectives, time scales and risk tolerance.
In some financial economics contexts "investment strategy" is used to mean a choice of investments. This usage is synonymous with the word portfolio.
The commonest strategies are growth and value investing. The former focuses on picking companies with opportunities to grow in the long term, whereas the latter prefers companies that are undervalued relative to their present profits or cash flows.
Because companies with strong cash flows are also those able to pay high dividends, investors looking for an immediate income tend to use some form of value investing.
Another common strategy, often used unwittingly, is momentum investing: buying whatever is going up, selling whatever is going down. The danger is that it leads investors into buying already overvalued shares and selling bargains. Momentum investors drive bubbles and crashes. It can be useful in conjunction with another strategy as it help investors time decisions, so that they buy or sell when the market is moving in their direction.
Contrarian investing is the opposite of momentum investing, doing the opposite of what other investors do. A contrarian would buy on a slump and sell in a boom, and would look to buy out of favour stocks and sell those that have risen sharply. It is also worth considering being contrarian on strategy: at times when everyone wants growth stocks you are more likely to be able to find opportunities in value stocks and vice-versa.
There are also many mechanical stock picking strategies, and elaborate techniques based on price charts. There is no evidence that "technical analysis" works. If it does work it should be possible to show statistical evidence for it.
Other mechanical strategies range from the very simple to the very complex. Again there is very little evidence that these strategies can allow you to perform better than the market (or an index fund) would have done, but for those with large portfolios it may be cheaper.
One of the most interesting mechanical strategies is the Dogs of the Dow (together with variants of it). It is also one of the simplest and cheapest.
There are also many short-term trading strategies. These tend to be high risk require a lot of work. Aggressive trading, and day trading in particular has made many people rich — it has also ruined many people. For the vast majority of people one or another buy and hold strategy is best.