I used select pine wood from Lowes for this project.
The top:
To fit 4, 15"x 15" Lego plates and a Lego piece trough on two sides, I decided to make the table 36" x 36"square. Frame out a 34.5" x 34.5" piece of 1/2" thick plywood with 1 x 3" wood- either with mitred 45 degree joint or end to end. However you choose to do it. Attach the plywood such that there is 1 1/2" above the plywood on top and 1/2" underneath. I used Gorilla Glue and 2" brad nails all the way around to secure.
This is it after I painted it black:
The raised platform inside of the base will be 30.5" x 30.5", to accomodate the 4 15"x15" Lego baseplates. Lego baseplates can't be butt up against each other tightly (or the legos won't fit properly), so I left some wiggle room for lego structures to be built on all edges. I used 1 x 2's as the supports inside of the base.
Once you secure the platform supports (I used glue and 1 1/4" screws), cut a piece of 1/2" plywood to sit flush on your supports. I had several scrap pieces that I made fit on the platform and secure it. I routed the edge to make it smooth. I didn't need to add a shelf in the edge, I just wanted to be fancy. Afterwards, I painted it all black with several coats.
The Drawers:
I made three different drawers of two different sizes. I wanted the top drawer to be more shallow, and then two deeper drawers for storage. The top drawer is made using 1" x 4" wood and measures 31.5" x 22 3/16" deep.
Cut two 1x4 at 31.5" and two at 22 3/16" and join the width to the lengths using pocket holes. Add a piece of 1/4" birch plywood to the bottom using glue and brad nails. I'd suggest cutting it with just a little overlap and routing the edge with an 1/8" roundover on all sides.
The second and third drawers were made using 1x 6 wood and measure the same as the top drawer. Repeat fitting the plywood to the bottom as before. All edges on top and bottom of all drawers were then routed with 1/8" roundover bit. When the drawers are all finished, give them a sanding with 120 grit and 220 grit sandpaper to make them smooth. Paint them if you want, but I chose to use a Minwax paste to protect them.
The Base:
The legs of the base consist of 4, 1x4" x 24" and 2 1x6" x 24" boards. the 1x6" legs run along the back side creating a drawer stop. Connect 1, 1x4 and 1, 1x6 together using pocket screws and glue as seen here.
The Drawer slides are just 1x2" boards attached 4.75" inches from top of legs, at 12.25", and at 19.75" down the legs. This gives enough clearance for the drawers to be pulled out using hands, instead of adding hardware.
With each side of the base complete, turn the table top upside down and put a finished drawer and the two base pieces down to ensure the correct measurement for the supports across the back. I have always found the "Measure Twice, Cut Once" mantra to be true. I apologize that I don't have a clear picture of the supports across the back, but they are 1x2" and set inside of the drawer slides you've already installed. These measured about 30". This allows enough clearance on either side of the drawer to slide freely in and out. You can kind of see the supports on the picture below.
The additional middle side piece was added as an afterthought, because the drawers would get a little off track when pushing it in so these were added to keep the drawers going straight in. It's gonna be used by a 7 year old after all.
When I was ready to attach the base to the tabletop, I ran a couple pieces of 1x2 across the top of the base and secured it with screws. Then I flipped the table upside down and attached the whole base to the tabletop screwing it underneath and into the bottom of the table. Make sure you don't use screws that are too long! You will probably only need 1" screws for this. Also, it's a good idea to use glue!
Attaching the Lego Baseplates:
Use some Lego pieces to join the 4 baseplates together and then use construction adhesive to attach them to the raised platform of the tabletop. This ensures that, when building, all pieces will traverse the plates seamlessly. Trust me, this is important!
Use weights or something heavy to hold down the plates under the adhesive dries.
I am so excited about this piece. If you are interested in having one built for the Lego Fanatic in your life, please reach out to me at She.Builds.NC@gmail.com to discuss the details.