In order to make anything out of pallet wood you will need some important relatively expensive tools, not to mention multiple pallets because you will likely break some boards or they will be broken when you obtain them. These are pretty common wood working tools that someone in your family could have or at least a maker lab in your area could help you. A very important thing to remember when trying this or any other scrap wood upcycling project, is that every step can be different than the last time someone did it. the quality of wood, thicknesses, splitting, paint removal. It all can have wide variations depending on your source of materials. The good news is that no one will have a table like yours!
Step 1: Acquire Tools
Chop saw (optional)
Sawzall with metal blade
Circular saw (optional)
Table saw (optional)
Planer (optional) not pictured
Finish nail gun
short finish nails
1" -2" screws
screw gun / drill
1/16 drill bit
paint, stain and or clear coat
Step 2: Disassemble the Pallet
In order to obtain a pallet for this table you must either work at a place that regularly gets and throws out pallets or know someone who does. This can be a warehouse, a machine shop, a big box store or as a construction worker. If you don't work at any of these places then talk to someone who does and get one or more through them. Often places sell back the pallets or use them to re-ship things so you can mostly only get ones that are broken. This is why a planer comes in handy if you have boards of different thicknesses and need to trim them down to the same thickness. Once you have obtained a pallet you can use a circular saw or the Sawzall to cut it into manageable pieces like in the picture.
Using the hammer and crowbar, work on prying the boards apart, then tap them back into their original position and some of the nails can be exposed enough to pull out with a hammer. If you are unsuccessful at prying apart the boards without risk of cracking them then you must use the sawzall to cut the nails. like i did with the board in the middle of the picture.
Do not use a blade for wood and metal, it can chip the teeth because it is meant to cut nails embedded in wood.
Step 3: Wood Prep
Once you have all the boards apart you may need to run them through a planer if they are different thicknesses from different pallets. Then sand them smooth.
If needed use a table saw to cut down a 4' by 4" board to 3" or so for example, to get rid of the cracked or uneven sides. (shown in pictures)
Be sure to remove all nails before doing this step because the blades can be destroyed if they hit metal and the sand paper can be torn or worn down faster if it encounters a sharp metal edge. Once the wood is all clean and straight you should seal the boards with a spray or brush on sealant, or you may stain the boards. I did a clear coat on my table.
For the legs I was able to use 2x4's from a disassembled pallet that was in pretty good condition but if you don't have boards already from some other project maybe, then you would have to buy one or two. If you must buy any wood ask the manager at Lowes or Home depot for a discount on warped, twisted or damaged pieces.
Step 4: Assembly
The length of the coffee table is limited to the length of the boards if you choose to arrange them as I did which comes out to 43". Otherwise you put more side by side in the other direction to make a longer table. Using a 1/16 drill bit you should pre-drill every hole where you will screw the boards underneath into a rectangle. my table came out to be 43" (inches) by 27" on the top and the rectangle underneath is 3' (feet) by 22 1/2"
The boards will be fragile and very dried out resulting in severe splitting if you drive in a screw without pre-drilling. Be sure that there is a 2x4 across the middle to support the table top later as seen in the picture. Due to the nature of using scrap wood and potential unevenness of boards used you will need to pick a "ratio" of table top over hang to rectangle size. ( If you do not copy my dimensions exactly) Having 3 2x4's at 21 inches long across the table provide enough wood to nail down the top. Using the clamps you should hold together the legs and use 2 screws per leg to secure them. Once you have confirmed that the table is not very wobbly then you are ready to use the finish nail gun to secure any boards you wish to have around the sides and the top. For the boards on the side it is a good idea to have them clamped down when nailing to help keep them flat.
Lay out the top boards to be sure that there are no undesired gaps or unevenness, and that the overhang is of the desired distance before nailing down the top.
Step 5: Finishing Touches
If you wish you may add brackets around the corners as I did. You can also glue back in the ends of the nails into holes on the boards.
Fill any holes with wood putty before painting the legs or don't.
Stain the top or don't.
Beat it up with a hammer and scratch it with a knife then seal it or don't.
Whatever you wish to do to the look is important though in order to make yours even more unique.
Good luck in all your future projects and endeavors!