To adjust for 100% audio modulation using an oscilloscope first of all you need to set the scope up so you can see the RF signal from the transmitter on the scope display.
All you need is a cheap TV scope, 6MHZ or so will work just fine.
You can buy a used scope, 20 Mhz used scopes are cheap and plentiful.
Be sure to get instructions with it, and that you will be able to use the equipment.

MCM Electronics has this inexpensive handheld unit

To set 100% mod:
Try to connect the negative or black lead to a ground or better the transmitter ground. Then the other scope lead is basically the antenna to capture the RF signal from the transmitter. Hang it somewhere away from metal until you see the RF signal. If you don't see the RF signal you may need to add some wire to the lead to act as an antenna. Also adjust the input sensitivity of the scope. Your sweep should be set appropriately (100,000) and turn you input level all the way up, or as sensitive as it will go. You can check the input level by touching the input lead, it should pick up noise from your hand and display it.

Once you see the RF signal feed a sine wave tone into the audio of the transmitter, 1000-3000 Hz is fine. Turn the sweep of the scope down to 1000 Hz or until you see the audio sine wave displayed. Then adjust your audio level as high as you can and still see a perfect sine wave. You are then at 100% modulation.

A scope can also be used as a field strength indicator.

See for an inexpensive modulation monitor, the unit can work with Part 15 transmitters. Update, we had heard from customers that radioassociates has not been building new product.