Whatever blows out, has to come in, otherwise you'd run out of air in the house.

Fans produce heat. Not a whole lot, but they do produce heat. Usually enough to rise the temp of the air blowing over the fan by about a degree. You want as much heat out of the house as you can get. By blowing out, the heat of the fan is carried by the air out of the house.

You want to remove the hottest air you can remove. Hot air rises, so the higher in your house you can place your fan, the better. If it's a 2-story house, put it in a 2nd story window. Seal around the fan as best as you can. You don't want the fan short cycling air around itself. Use an old blanket or whatever.

With the fan in place and running, you've now created a condition where the pressure inside your house is lower than the pressure outside your house. The pressure outside wants to equalize the pressure inside, so any window you open now becomes an opportunity for the higher outdoor pressure to push cool air inside. In truth, you want the air to flow as freely as possible, so the more windows you open the better. Think of it as trying to blow air through a straw. The bigger the straw the easier it is and therefore the more air you can blow through it.

A standard box fan works best.