First - login to the MyScouting page using your username and password.
If you don't have one, you've got other work first. You need to create an account, take the Youth Protection Training, submit an Adult Application to the Troop, wait to be registered, then come back here.
After you login, you see the page below. The next step is to select the option to work on Tour Permits.

Once you get it, there are two areas of the screen. On the left side, you select which tour permit you want to work on. You can have several pending tour permits going, and you might have several submitted, waiting for the permit to be issued. This side is also where you create a new Tour Permit to start working on it. On the right side are a variety of tabs related to information for the Tour Permit. See the screen shot below:

So, first, you need to create a new Tour Permit to begin work.
On the left side click on the Create link. Enter the name of the new tour permit. I like to include the destination and year information. Click on all the pop-ups confirming you want to create a new permit.
Next, select that Tour Permit to begin working on it. At the top of the screen it indicates which tour permit you are currently working on.
If you have not created Tour Permits before, you will need to enter (at a minimum) the information regarding vehicles to be used, and the current training for those adults participating. You might want to enter all known information at this time, while you have it in front of you. This will save time for future Tour Permits. The vehicle and training information stays available for future permits.
Click on the "Enter Vehicle" tab at the top. Enter all the vehicle information. They want vehicle make, model and year. They want the number of passengers possible, the owner's name and driver's license number (Note: owner, not necessarily the driver). Then they want the three standard insurance values: per person coverage, per accident coverage and property liability.
For example:
Dodge RamVan/1985, 7 passengers, Bob Smith, A1234567, Yes, 500000 per person, 1000000 per accident, 500000 per accident
Be sure to click on the "Save" button for each entry. When you are done entering vehicle information, be sure to click on the "Update my Permit" button at the bottom of the screen to save all the records for this permit and future use.
Now enter the BSA and non-BSA training for adult participants. Again, if you enter everything now, it makes things easier for future Tour Permits.
Click on the "Enter Training" tab at the top. This time you enter the person's name, age, select the type of BSA training and enter the date the training was completed. Be sure to use leading zeros on the month and days section of all dates.
For example:
Bo Edward Smith, 49, Youth Protection, 04/10/2010
Bob Edward Smith, 49, Safety Afloat, 04/10/2010
Again, be sure to click "Save" for each entry. When you are done, be sure to click on the "Update my Permit" button at the bottom of the screen to save all the records for this permit and future use.
Do the same for the non-BSA training entries.
For example:
Bob Edward Smith, 49, CPR, 03/10/2009, AHA
Richard Jones, 63, Wilderness First Aid, 04/10/2010, ASHI
Again, be sure to click "Save" for each entry. When you are done, be sure to click on the "Update my Permit" button at the bottom of the screen to save all the records for this permit and future use.
Now you are ready to complete a Tour Permit. At the top of the screen be sure it indicates which tour permit you are currently working on. Select the tab that says "Step 1".

In the middle of the screen click on the button labelled "Edit Tour Information".

Click the box indicating you have received parental approval for the boys. Then fill in the Insurance and Attendance information:

Fill in the starting point, the destination and the dates, being sure to including leading zeros, again. More detail makes it easier for the Council to approve the permit on the first request. Check the Tour Permit name and say what (why) we are going on this trip. Pull down the Tour Type and select the correct entry. A day trip, picnic, etc is a "One-Day". One or two nights is a "Short-Term". Three or more nights in one spot is a "Long Term", driving to many spots is a "Touring".
Check the boxes on the activities that will be included, Swimming, Boating or Climbing.
Be sure to click the "Save" button.

Now near the bottom is a button called "Edit Leadership Information".

Click on it. Enter the names, ages, phone numbers and e-mail addresses of the two adults that have agreed to be in charge of this trip. At least one of the must have current Youth Protection Training. Both must be registered with the BSA. Click on "Save".
Next click on the "Step 2" tab at the top. Check all the boxes to indicate we agree to comply with BSA regulations regarding these activities, and then click "Save".
Now continue by clicking on "Step 3" on the tabs. Here you will be entering your Tour's Itinerary. This should include all legs of travel, and detailed routes, where possible. Include the starting point of each leg, pull down and select the closest method of travel. Use Google Maps to find accurate distance estimates. Describe the routes in detail. For example: Santa Barbara to Mojave might be described as "Hwy 101S to Hwy 126E to Hwy 5S to Hwy 14N to Hwy 58E". And the reverse for the return path. Be sure to include a description of the overnight location, and whether the lodging is reserved or permitted. Keep adding legs until you complete the trip. Hit "Save" to enter each leg.
Next, we select all the vehicles that will be travelling on this Tour Permit. Note that vehicles not selected are not part of the BSA Trip, and will not be covered by the BSA policies or Council insurance. This is important if families might be travelling separate, but arrive for an event. Other Boy Scouts should not be sent in these vehicles unless the parents are clear that vehicle is not part of the trip, and will not be a BSA tour.
Click on the box selecting the vehicles on this page that will be travelling. Select the "Save Transportation" button. Then select the 2nd page near the bottom to see additional vehicles. Select all on this page that are included, and again click on the "Save Transportation" button. Continue through all pages of possible vehicles, selecting them and "Save Transportation" before continuing to the next page.
Now select "Step 4" from the tabs at the top. Similar to vehicles, we check all the boxes of the adults that are going on this trip. Be sure to select all the boxes of the Tour Leader and the Assistant Tour Leader. There must be a minimum of YPT, and the required training for all activities planned (i.e. Safe Swim Defense if swimming is planned). Be sure to click on the "Save BSA Training" before going to the second and successive pages of training records, or they don't get registered.

And finally, select the non-BSA training for the individuals going on this trip:

One more time, click on "Update my Permit" for good measure.
Review all your entries to make sure they are correct, and registered with the system.
Now, finally, submit the permit by clicking the (strangely) first button on the page.

If there are any problems, the system will pop-up warning about things that need fixing. Some can be ignored. For example, you are supposed to submit a Tour Permit a minimum of two weeks before the event. It will warn you. However, it doesn't stop you from submitting anyway. You just might not have enough time to fix errors.
When it is accepted, you and the tour leaders will get e-mails confirming your submission. When it is confirmed by the Council office, you all will get an e-mail with the Tour Permit attached. Print that one.