Trying to actually find clues from the Tenkan line for future price movements should not be that difficult as this line is the first to react to any changes in price. Tenkan line is used in the following ways:
one approach is to look for the Tenkan as possible support and resistance point for current price. If one takes into consideration how it is calculated, averaging the previous nine candles highest high and lowest low, then the result should be quite a powerful support and resistance. The higher the time frame, the stronger the support/resistance. Come to think of the importance the time frame plays: if you are looking at the five minutes chart then look for Tenkan to be pierced quite often. But by the time you are moving on the hourly, daily, weekly and monthly chart, that looking at current price action on the lower time frames but taking into consideration the higher time frames level for the Tenkan should work pretty good in identifying strong support/resistance areas;
another approach is to look at Tenkan in comparison to the other elements of the Ichimku indicator:
Kinjun, cloud and Chinkou. When Tenkan and Kinjun cross, that is a bullish/bearish sign, depending of the direction of the general trend. When Tenkan approaching the cloud in front of it, that should be watched as usually price reacts when such a thing is happening. Again, the higher the time frame, the better.
Also, when Tenkan is breaking above/below the cloud that should be interpreted as a bullish/bearish move and should be treated with respect.