In C#, the "scope" of variables is well defined. In your code, the textures are created within the scope of the method "LoadContent" and then are deleted once the method is done. What you need to do is place the textures at a "class" level like so:
//outside of the method, and in general, should be placed near the top of the class
Texture2D tileStart;
Texture2D tileCrossJunction;
Texture2D tileTJunction;
Texture2D tileCorner;
Texture2D tileHallway;
Texture2D tileDeadEnd;
Texture2D sqrPlayer;
Texture2D sqrBaddieSmall;
Texture2D sqrBaddie;
Texture2D sqrBaddieLarge;
protected override void LoadContent()
{
spriteBatch = new SpriteBatch(GraphicsDevice);
//be sure to remove Texture2D from these
//this will insure that the "class" level variables are called
tileStart = Content.Load<Texture2D>("tile_start");
tileCrossJunction = Content.Load<Texture2D>("tile_crossjunction");
tileTJunction = Content.Load<Texture2D>("tile_t-junction");
tileCorner = Content.Load<Texture2D>("tile_corner");
tileHallway = Content.Load<Texture2D>("tile_hallway");
tileDeadEnd = Content.Load<Texture2D>("tile_deadend");
sqrPlayer = Content.Load<Texture2D>("sqr_player");
sqrBaddieSmall = Content.Load<Texture2D>("sqr_baddie_small");
sqrBaddie = Content.Load<Texture2D>("sqr_baddie");
sqrBaddieLarge = Content.Load<Texture2D>("sqr_baddie_large");
}
Once you have done that, the "scope" of the variables will be at the class level, and you will be able to use them from other methods within the class.
In other words, there is no way to access a variable that is declared within a method from outside of that method (without passing it as a parameter to another method of course), the tutorials you are looking at might just be short hand, and expecting you to do it "properly".