There are 2 places to collect enough data to create the PRAWN suit that I have found: the Aurora (the easiest and the most likely as you will get to it early on) and a broken section of a ship approx. 800m N (towards the bulb forest) of the escape capsule you start on in the game (much harder to get to as it's further away, deeper down, on a floating island, and there are large monsters nearby).
Scanner is an obvious requirement. Radiation Suit. You will also need the laser cutter; if I remember correctly, I started finding parts for it near Lifepod 17 (don't recall as it's been a while). Propulsion Canon (like the laser cutter, I don't recall where I found the parts to scan for it; it's more about searching wrecks until you have the blueprint as is common in the game). Fire Extinguishers (some can be picked up along the way). Batteries (some can be picked up along the way).
Ideally, you have the laser cutter previous to your first trip to the Aurora (I didn't); if not, it's all the same.
Enter the Aurora from the front. There is a lower section that will require use of the Propulsion Canon to enter the door. Go down the hall, into the water, into the room with the sparks, look left from the door you entered and the door on the right will be the one to cut. You'll get to a panel you'll interact with. Swim up, then look for an opening, swim through some pipes until you service into the Prawn Bay where you'll be able to scan the 4 needed parts. Go into the Living Quarters as well and use code 2679 to get into the Captain's Quarters.
If you go to the upper level you'll also repair the reactor at the same time; so, if you want to do all this in one go it's best to go this direction. Enter the Aurora from the front. Go up the ramp on the left. Once at the top a beam will take you around to the door you need to enter. Down the hall until it splits left and right. To the right is an admin room that will give you a code the door you will be entering as well as a few other things. Leave the admin room and go straight to the other end. Move the obstruction with the Propulsion Canon. Code 1454. Down the hall. In this bay there are a few items to scan for later use. Down the lift and into the water. When you exit go slightly left into the hall to get to the reactor to repair the meltdown. Be careful of the bleeders as they attach to you and will kill you. Bash them a few times and they die ( may need to put away whatever is in your hand, if anything, to do it).
Once you've repaired the reactor, go down the hall until the intersection, take a right and cut the door. There will be a door to the left in there. Down a hall on the right will be the door to cut through to enter the Prawn Bay. Again, up to the Living Quarters and Captain's Quarters is 2679.
Building the Prawn:
Taken from sefjwm on PS3imports.org
Mobile Vehicle Bay - 1 x Titanium Ingot (10 x Titanium), 1 x Lubricant (1 x Creepvine Seed Cluster), 1 x Power Cell (2 x Battery (2 x Acid Mushroom, 1 x Copper Ore each), 1 x Silicone Rubber (1 x Creepvine Seed Cluster))
Prawn Suit - 2 x Plasteel Ingot (1 x Titanium Ingot (10 x Titanium)), 2 x Lithium each), 2 x Aerogel (1 x Gel Sack, 1 x Ruby each), 1 x Enameled Glass (1 x Stalker Tooth, 1 x Glass (2 x Quartz)), 2 x Diamond, 2 x Lead
Right, hopefully that's helpful. Obviously, there is a lot to this game with going back and forth, collecting, exploring, and so on. If there is anything to clarify or add or whatever let me know.
Subnautica Wiki is also very helpful if you're still lost about things. I've been using it a bit.