New Pantheon project

Create a new Site on Pantheon with Drupal 7 installed.

In the Sites version of the site you're working on, make sure all the changes you want are pushed.

In the Projects version of the site you're working on, pull changes to the branch you want to push to Pantheon.

In the Projects version of the site you're working on, modify scripts/build.sh to add the SITENAME and the GITREPO. The GITREPO will look something like ssh://codeserver.dev.[LOTS OF STUFF]/~/repository.git. You can find it by clicking the Git button on the Code page of your Pantheon Dev Site page.

Type:
./scripts/deploy.sh

You'll get an error related to settings.php, but if you drop down a level, you'll see a folder generated by the deploy script. Go into that folder, and in sites/default/, run:

cp default.settings.php settings.php
git add settings.php
git commit -m "settings.php from default.settings.php"
git push

Go back to your working Projects directory and again run:
./scripts/deploy.sh

On your Pantheon dashboard on the Code page, change Connection Mode to SFTP, then click the Connection Info link next to Clear Caches. Grab the text in SFTP Command Line and paste it in your terminal. It should look something like: sftp -o Port=2222 dev.[LOTS OF STUFF HERE].drush.in

Connect to your server, and in code/sites/default, run: chmod 755 settings.php

Click Visit Development Site and install your site with the correct profile and settings.

For the database settings, check your dashboard. You'll need to enter the database name (pantheon), username (pantheon), password, server, and port.

When you want to run deploy.sh again to commit more changes, you'll need to change from SFTP mode to Git mode.