You don't say which linux or desktop environment you are using so......
I assume your using X11 so using your file manager, right click the jar file, go to the permissions tab and check the make executeable box.
If you can't, you may need to change ownership which will require root permissions, try (gnome)alt f2, then type gksu nautilus in the box and hit enter continue as above with permissions and ownership...(kde) kdesu dolphin, and continue.
In a terminal you could cd to /home/tyler/Desktop/Tyler's Stuff/ then type chmod +x minecraft.jar
In a terminal type man chmod and man chown for a help file. You can always use google.
Welcome to Linux!