The easiest(?) way to connect a garage to a house on foundation goes something like this:
Lay the driveway and extension piece.
Build the walls around the garage as normal.
Next to the garage build another room 2 tiles wide - you won't use this room, it just acts as a way of connecting the two buildings.
Now build the rooms of your house WITHOUT foundation, first floor only for now, no windows, doors etc. yet.
Use CTRL-SHIFT-C to open the cheat console and type boolprop constrainfloorelevation false.
Use the foundation tool to 'fill in' the rooms, one at a time, but not the garage or the 2-tile-wide room next to it. The view will change as you do this, so you'll need to switch down to the foundation view after each room.
When this has been done, you'll see that the walls surround the foundation and are only the same height as the foundation now. Use the wall tool to rebuild the rooms on the ground floor.
With the cheat still on, use the terrain levelling tool to match the height of the garage and the ground floor rooms. If you don't, the roof will look weird. You may have to play around with the terrain levelling tool a few times to get the wall heights as you want them. Also, the walls may look OK until you come to place the garage door, then the upper part of it will disappear. Experiment until you get the best effect.
Then turn off the cheat and build any upper floors.
Decorate / furnish as usual. Paint the outside walls with paint or stucco rather than a stone or brick pattern, otherwise the reshaped sections of wall will really show, and they don't look too pretty.
The question inspired me to build a house with attached garage - if you have all the EPs up to FreeTime you could download it here ---> Tutorial.zip - it contains a bit of custom content, though, so it's a bigger file size than normal.
Here are a couple of pics so you could see what you're downloading. It's not furnished, by the way. I found a use for that 2-tile-wide room, too.