For my current school I completed the online application and uploaded my credentials and a cover letter. I interviewed for both the elementary and high school via Skype. I think taking the time to create personalized cover letters for each division, addressed to the principal in each, and tailored to the positions I was applying to may have helped get my application noticed. But then again, we have a pretty awesome HR Department that does a really good job, so who knows.

AAS Moscow does a good job:

1) meet you at the airport
2) take you to your furnished apartment where you have all the necessary basics - linens, dishes, cookware, etc. until your shipment arrives - also a welcome basket of food staples including fresh veggies, fruit, eggs, coffee, etc.
3) welcome dinner at one of the admin or co-worker's flats in your complex the first night
4) school orientation begins the day after you arrive and it's really a combination of school and city orientation
5) several new hire dinners within the first 2 weeks - one at the director's house and one at a restaurant
6) optional excursions about town to familiarize you with the metro system, shopping (IKEA, etc. to pick up things), dining
7) optional tours of museums, the Kremlin, riverboat cruise, etc. begin almost immediately and run throughout the year

The first day of orientation I received a sim card for my cell phone. You can get a second one for your spouse, iPad, etc. This has been one of the best perks since you bring your phone, pop in the new sim card and then they deduct usage charges from your paycheck and you never have to worry about paying for a plan or dealing with the cell phone company. My charges have never been more than $5 a month. We also received our settling in allowance (in rubles) the first day of orientation, so we had local currency right from the start.

I am currently teaching in Moscow. For the moment, things are much as they were when I arrived. The only differences I have seen or even heard about are a few more planned rallies and demonstrations than usual. We are always given notice ahead of time - the who, where, and when. I just avoid those areas during the specified times. For now, everyone is staying on high alert and security is a little tighter at the embassies, but it's anyone's guess whether there will be any major problems in the near future.

My school provides the same lump sum to each teacher, paid half in the fall and half in the spring. Travel or don't - either way you get the money.