How do I download Minecraft 1.7.10 on my MacBook Pro

You have an older version of Java 6, go here: Java for OS X 2014-001 and download the latest. Do be aware that this download is for OS X 10.7 (Lion) or higher. When you have successfully install this version, the result of a "java -version" command will be this:

java version "1.6.0_65"

Java(TM) SE Runtime Environment (build 1.6.0_65-b14-466.1-11M4716)

Java HotSpot(TM) 64-Bit Server VM (build 20.65-b04-466.1, mixed mode)

Right here: https://s3.amazonaws.com/Minecraft.Download/launcher/Minecraft.dmg

On the Minecraft.net page, hit the link on the right and the page should show you the Minecraft.dmg. If it does not, hit the "Show All Platform" link, or use the link I provided. Enjoy!

A reminder: you will need Java installed in order to play Minecraft. Either the "legacy" Java 6 that Apple provides or Java 7 from Oracle. Java does not have to be usable by a web browser for Minecraft to work, and I strongly recommend that you turn Java off for your web browser as it is a popular way for malware to get onto computers. If you must use Java in your web browser for reasons other than Minecraft, at least use Java 7 as it is more actively updated than Java 6, which is pretty much at end of life for support.

FYI, I run Java 6 and do not have it available to any web browser. Minecraft works fine in it.

Open up a terminal (in finder "Applications" then "Utilities" or type "terminal" in spotlight). Then type (without the quotes) "java -version" and hit return, copy and past the output.

Paste it to your reply here so we can see what version of Java you are running.