RSI (the Relative Strength Index) gives you a reading of the momentum of price movement. If the RSI is pointing strongly upward and it is still below the 70 thresholds, then the price still has more way to go up. If it is pointing strongly downwards and it still has not reached the 30 thresholds, then the price still more room to fall. This does not mean, however, that the price will reverse direction once it reaches overbought or oversold territories. Markets usually extend their uptrends and downtrends. It is the very definition of a trend that it is a condition in which markets continue to go higher (or lower) even after having reached overbought (or oversold) territories and stayed there for long.
The RSI can be used in two different scenarios: trending markets, and sideways markets. In trending markets, such as a rising trend, it is recommended to wait for the price to go towards the trend line and the RSI to enter into oversold territories and then wait for both to reverse. Once the price bounces off of that line and the RSI leaves the oversold territories, it is a good opportunity to catch that trend.
In sideways, the same strategy can be used with the horizontal lines restricting price movement. You simply wait for a reaction to the trendline from the price and a switch in tone from the RSI to establish a position. If the price goes against you and breaks out of the sideways movement, it is a good opportunity to close the earlier position and enter into a new trade to catch the trend.