Can I use images showing up in Google search for my presentation slides without violating any copyright? I am teaching a freshman science course for the first time and I am doing also outreach activities in high schools. To be able to attract the young generation to science one has to connect the concepts with everyday applications.

So I build my power point slides using pictures from the textbooks which we officially use. Unfortunately when one does a Google search on any subject by images, one gets much more appealing and fascinating pictures. Some of these pictures are even related to simple applications which are explained in popular science sites on very recent discoveries. The problem is that I cannot use those pictures from Google sites in my slides because they are copyrighted.

What should I do then? Should I stick to the boring-looking textbook pics to avoid copyright problems, or bring life to my course by using images Google shows up (but then I might go to the jail!)?

Is there something that says one can use images shown by Google for educational purposes with no copyright issues?
You can use images showing up in Google Search if and only if the license allows for it.  Therefore, you might be interested in Advanced Google Image Search, where you can search by copyright status. More information about the Usage rights search can be found here.

For example, here are freely useable images searching for "Mars".  Notice how many of them are from NASA or the Wikimedia Foundation.

And here is an example searching for "IBM".

Note: See the important remark by @jb. in the comment below
 —
 you should verify with the original source (1) that the picture really is free to use, and (2) under what conditions

Good luck and enjoy!