I am installing a ge #15070 basic timer and there are 3 wires. Which wire do I attach to the ground?

well, without being there I would say they are the power wires.
Black usually goes direct to the switch then the other wire off the switch goes directly to the motor.
White is the neutral/ground wire it will be in a bundle of probally 3 and the Green is your secondary ground which without it you have a better than good chance of being shocked if the unit gets shorted. so it could be attached to a bolt on the motor.
What colors are the wires on the motor? are you replacing it or the power cord? need more input.
I have not worked on this model or make of vacuum and would need to research it and find bigger pics as I get older my eyes are not as good as they once were.

1) If you are replacing T103, the T103 can be wired many different ways. Not all wiring diagrams are supported by GE 15600 replacement timer that fits into Intermatic box.

2) Double check your T103 terminals
T103 terminals should be A 1 2 3 4
If terminals 3 and 4 have wires, then GE is not correct replacement.
You can buy repair parts for Intermatic timer
http://waterheatertimer.org/How-to-wire-T104-Intermatic-timer.html#T103

3) GE has terminals 1 and L which are connected by brass bridge. If brass bridge is removed, add a jumper wire and connect terminals 1 and L
GE has terminals 1-L X 2

4) Typical GE 15600 wiring shows on following link, in addition to links for parts and manual:
http://waterheatertimer.org/GE-timers-and-manuals.html#15306

White wires on terminal A connect to terminal X
Black wire on terminal 1 connects to terminal 1
Black wire on terminal 2 connects to terminal 2

You might not be able to use that switch in your configuration. It appears that the power was run to the light and only two wires were run back to the switch. The old switch only closes to connect those two wires completing the circuit at the lighting fixture, but you need a hot and a neutral to operate the electronic switch that you have.
Gary

1) GE 15086 is not a 3-way timer.
GE programmable timers are for single-pole switch replacement only. I have tested this timer, and own several GE timers, and many other brands.

2) Open following link to identify timers that work for 3-way switching.
http://waterheatertimer.org/GE-timers-and-manuals.html#15071

3) After buying correct timer, then you need to review wiring diagrams carefully because the timer replaces 1 of the 3-way switches, but other 3-way switch has to be wired exactly right to match your brand of timer.

4) Links on page above show manuals for each of the 3-way timers. Compare wiring for each timer with Intermatic wiring that you are replacing, because Intermatic is wired differently than Aube.

5) Or just buy another Intermatic ST01C or EJ500 or EI400, etc, and wiring with change out 1 for 1.

6) Add a comment for more free help.
Also take advantage of fixya expert assistance live.
For a price, expert works with you while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

I am commenting on things are here in the u/k not u/s which is not the same but i hope this is of some help.......From the wall black and white ,this is a switch wire which is on or off, i would link this to white to white , black to black or black to red with the rest left unconnected,,,,,Check to see if you have fitting instructions indicating what wire goes where....Good luck

1) If you have chronic problems with electronic timers, then circuit is suspect. Buy cheap circuit analyzer and plug into same outlet. Try timer on different outlet on different circuit breaker. Change Load (lamp, fan) to see if same problem occurs with different load.

2) Maximum load for GE 15091 is 600 watts incandescent. There is no HP rating, so timer probably not made for motor loads since motors draw high initial amperage. For heavier duty timer, with 1250W incandescent and 1/3 HP, select Woods 59201.
http://www.amazon.com/Woods-59201-Appliance-Grounded-3-Prong/dp/B001Q9EFTQ

3) I have tested GE timers. They are made well.
The 15091 is sold under different brand names, so it is successful design that's been around a while.
http://waterheatertimer.org/GE-timers-and-manuals.html#15091
http://waterheatertimer.org/Woods-timers-and-manuals.html#59201

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

GE 15071 is single pole only.

Open following link to see GE 15071 timer, on-line manual, and steps for wiring:
Link also shows timers that work for 3-way switch and include links to those timers and manuals:
http://waterheatertimer.org/GE-timers-and-manuals.html#15071

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

GE 15086 7-day programmable timer will not work for 3-way switching.
http://waterheatertimer.org/GE-timers-and-manuals.html#15086
It is possible to wire GE timer in place of a 3-way if you tape the other switch in one position.
Add a comment if you want help with that wiring.

There are several 7-day programmable timers that can be wired for 3-way. Each of these is wired slightly differently, and you have to look at wiring diagrams carefully. But they are completely do-able.
Links below go to pages that show manuals and information.
Aube T1032
Aube T-1070 7 events
Aube T-1073 21 events
UPM ETW193 20 events
UPM ETW350
Brinks 46-1022
Intermatic ST01C 40 events
Intermatic EJ500 40 events

Add a comment for more free help.
Also take advantage of fixyas phone service.
For a price, fixya expert speaks with you over phone while you work on timer.

I would guess that the black wire on the timer is the power in and blue is the power out to the fan (hook it to the black wire going to the fan) The other colors are right.

If it won't work without a ground wire, but still works with one, then you must have a ground/earth connection to make it work - it sounds like there is a safety device that needs an earth to release, you could almost certainly bypass this relatively easily, but it will be there for a good reason and that would be dangerous. Bearing this in mind, regardless of which 2/3 prong adaptors you use, without an earth connection it will not function without risk probably of electric shock from the case or damage to the vacuum, else the safety device would not be there. Get an electrician to your home, and make him install grounded sockets where necessary (should be all, but at least get a couple). Ungrounded/unearthed domestic power sockets at all domestic AC voltages are lethal eventually, to man or machines. A lot of devices don't need an earth, but especially something with a big motor or a metal case usually does. At least ask a local electrician what he thinks. If you want to do it yourself, an Earth circuit in your home is not too hard to achieve if you have basic wiring skills (and access to the ground floor), but most insurance would dislike the idea - if you want to - post again and I may talk you through it. Hope this helps :) Please be careful :(