If you are starting with S4S 1x10s from you local big box store, you can skip a lot of the planing steps here. I am working with rough sawn pine.

First I need to rough cut this board to manageable sizes. A lot of personal preference comes in here. I want to maximize my productivity. For me that means cutting the boards into a 32" piece and a 22" piece. Here are some reasons why
 - I need (2) 15" pieces, and (2) 10" pieces. I'd rather not prep 4 separate pieces, and I'd rather not prep one 50" piece.
 - I could have cut 2 equal length pieces so I can get one 15" board and one 10" board out of each; and that is my preference, but I chose to work around the knots rather than include them. 
 - I cut the rough lengths so I would have at least an inch extra for each final piece. This will allow me to deal with any end checking or other hidden defects. 

Why not cut the lid and bottom while I'm at it?
Wood movement. My shop is not climate controlled and my weather is variable at the moment. From warm and dry, to hot and very humid. I've found it best to only prepare the pieces I will be able to work and assemble within one or two days time. 

After measuring I mark the board with a knife and then darken it with a pencil.   

I then secure it to my bench top using holdfasts.

I am using a Ryoba to complete this cross cut. I like to start at the edge of the board closest to me. I work on a steep angle at first. This lets me keep track of the vertical and horizontal lines so my cut has a good chance of being straight and plumb. Accuracy isn't super important here because precision cross cutting will be done later. However I find this to be a good opportunity to practice my sawing as it's consequence -free

If you are using a western style saw, you process will be different.

Once I establish the cut, I use a shallower angle and saw through. Repeat on the other and I am ready for planing. 

To flatten the board I am going to use the following:

 - Jack plane (heavy set). A scrub would do well here if you have one
 - Jack plane (lighter cut)
 - Jointer plane 

My bench is not equipped with vises, but cross grain planing operations are still very simple. I have the board up against a planing stop at one end, and a doe's foot at the other. 

Also note that I am left handed so if this set up looks backward to you - it probably is. 

I then like to see what I am working with using winding sticks. I got lucky here. Lots of cup (easy to deal with), but very little twist (harder to deal with). I like to plane the board with the crown facing up so it sits solidly on the bench.  This article explains how to use winding sticks, how to make your own, and how some things in your shop can double as winding sticks in a pinch

Now I take cross grain shavings with my heavy set jack plane. I work slightly diagonal across the grain along the length of the board until all of the saw marks are gone

Once that is done I check again for twist. What little there has been worked out 

Now I clean up the surface from the rough cross grain planing, and do the initial flattening. I still use my rough set jack here. It takes thick, but clean and even shavings to speed things along 

I use my winding sticks to check for flatness. The left side is still a little low, so I'll I'll address that with the jointer plane 

One of the things I like about wooden planes is how easily they glide across the surface. Metal planes will glide much easier if the sole is conditioned with oil or wax. I always keep this little box of wax and a small rag close by.

After jointing, I like to go over with a small smoothing plane. I'm not too concerned about surface prep (yet), but because a jointer is so large, it can miss little low spots . When I get full uninterpreted shavings from the smoothing plane, I am good. Now that I have one face jointed, I put the piece into a thickness planer to bring it to final thickness. I do not enjoy manually thicknessing boards, so I let the machine do the "donkey work" as Paul Sellers would put it. 
If you are going to thickness by hand, It's similar to the procedure detailed below for the edges. Also this is a good video that demonstrates the whole process done by hand.

With the 2 faces square and the board to the correct 3/4" thickness, I am going to square one edge. Since this board is fairly short, I don't feel it is necessary for me to use anything but my jack plane. I like to remove the rough edge first, then plane a small belly in the middle. Now I go from edge to edge. When the plane takes a full shaving, I know it's (probably) straight.    

Once I am done, I first check to make sure it is square to the faces. I check in several locations using a small precise square 

Then I check to see if the board is flat. I know my workbench is, so I use that as my reference surface. The first 1/2" on the left is a little shallow, but that's getting cut off later anyway so I'm calling this good

Ripping by hand is another task that some planing ahead pays off. I am going to rip these before I crosscut them to their final length. This way I only need to do 2. The boards need to be 9 1/2" wide, so I use a ruler to set my panel gauge to 9 1/2"

I then use my freshly jointed face to reference the fence of gauge against, and strike a line on both faces. I make multiple passes here. I like a deep line

Here you can see the mark left by the panel gauge. Also there isn't much material there. Rather than saw it off, I'm just going to plane it. 

Follwoing the same basic process as above, I secure the piece to my workbench

I take heavy shavings until I get close to my line.

This is why I like a heavy gauge line. It is very visable.

I now use my jointer plane with a lighter cut and plane until I hit my line on both sides. I know when I hit the line because the fibers that were cut with the panel gauge come off in a continuous string. When done, check for square and straight like above.

The same procedure is used if you mill the pieces to final thickness with hand tools; but for the face of the boards instead of just the edges. 

With the pieces flat, square, and to the proper thickness and width, it's time to cross cut them to the proper length. I will be using my Ryoba again, a ruler (or tape measure), a square, and a shooting board. 

Before I measure for the initial cross cut, I take one edge to the shooting board to create a reference. Like with the initial cross cutting, I use the same approach. Accuracy does matter this time. Take your time. Once cut, take the piece back to the shooting board and square/clean up the other edge.

Use the piece you just cut as a reference for the other one. Be sure your reference edge on the piece to be cut has been squared on the shooting board first. Exact measurements are not important at all. What is important is the pieces are exactly the same size as each other. If they end up being a little shorter than the plans, that's fine as long as they are both identical.

I make a nick with the knife at the top and bottom edges. I then put the knife in one of the nicks and bring my square up to reference it.

After that I have the box carcass ready for joinery. 

Before moving on to the next step, I like to take this opportunity for some housekeeping. I use a small paintbrush to clean the dust and chips from my planes, then lightly oil or wax them before returning them to the till. 

I also like to clean up all the shavings and other scraps so I can start fresh with the next phase - cutting the dovetails.