If I remeber rightly, the JRE install files are self extracting files. Unless you are running the 64 bit version of Ubuntu, you will need the one just called 'Linux'. Download it to somewhere and then open up a terminal and run:
Replace jre.version.bin with the name of the file you downloaded.
Not sure what will happen then, it will either install it, or create a directory with instructions inside.
EDIT: Beaten to it! Following the official instruction is probably the best way