You can have regular oscillating fans in the tent/room. I like to have one at the top and one at the bottom circulating the air.
This is air circulation, it is different from air exchange where you need to have fresh air from outside the air coming in and hot/stale air from inside the area blowing out.
For most tent grows, the only thing you need is an exhaust fan. Specifically a high velocity inline fan. You mount this high in the room so it sucks hot air out. It also has a secondary purpose and that is to draw air in by creating a negative pressure in the tent. If you cut a hole on either end of a box and sucked air out from one hole, air would be drawn in from the other hole to equalize the pressure. If you didnt have an intake, the cox would collapse due to the outside pressure being greater than the box pressure.
You need an intake port at the bottom of the tent at the opposite side of the exhaust. The hole should be bigger than the exhaust so that it can draw in enough air to equalize the pressure. You dont need a fan here, the air will be drawn in passively. This is called a "passive intake"
There are 2 options with air cooled hoods. You can run a dedicated intake/exhaust port and fan for just the hood. That would be drawing cool air in from outside the tent, through the hood and then exhausting that hot air outside the tent. The air in this case never touches the grow room and doesnt need to be filtered for odor. This is the best option but not always attainable.
If you only have one fresh air intake, you dont want to use it to cool the hood because then you would not have any intake ports to draw fresh air in and exchange the air in the room. In this case, you can leave the intake port as a passive intake and cool your hood with air from inside the room.
Here, the air would need to be filtered first. Otherwise you would be exhausting grow room air out of the tent. If odor control is of any concern, this wouldnt work. Also, it is a good idea to have a filter before your hood so as to not draw dust or other particles into your hood where they could accumulate on the bulb or glass. So you would have a carbon filter inside the tent with ducting running to one end of your air cooled hood. On the other end, you would have ducting running to your exhaust fan. The exhaust fan would then pull air through the filter and hood and blow it outside the tent.
If you run a filter before your hood, I would get a fan with a higher CFM than you need. The filter and ducting will add resistance and you want to be able to pull air easily through both. You can get a fan speed controller to slow it down to optimal speed and also cut down on noise. I run my 6" fan at about 75% and it significantly cuts down on the noise while still easily pulling air through both the filter and hood.
Get a fan that matches the size of your hood and filter. So if you get a 6" filter and 6" hood, dont get a 4" fan. Avoid reducers if possible. They greatly reduce efficiency and increase air noise.