How to shorten a maxi skirt while keeping the bottom hem?
The biggest problem is getting a straight hem line. There are skirt hem markers designed specially for this purpose. They have a little chamber with powdered chalk in it and a little bag bellow with which you blow a fine line of chalk onto the skirt.


If you don't have one of these, you either need a sewing bust (set to your corect proportions) or the help of a second person. 

Additionally, you need some tool to measure the length of your skirt. A rigid ruler works fine, but in my experience something that can stand upright and has an adjustable height works great, like a mini camera tripod. You can put a water-soluble fabric marker on top to easily mark the desired length.


There are 2 basic ways to shorten the skirt: either cut the original hem off and sew a new one instead or pleat the fabric to create a blind hem without cutting. If you don't want to sew at all, you can create a blind hem with fabric glue instead, but I've made the experience that this glue dissolves in the washing machine (despite all claims by the manufacturer) or stays visible even after drying.

If you're ok with cutting the fabric, follow these steps:


Wear the skirt and the kind of footwear you like to wear with it (can be barefood, too)
Stand on some kind of podest, stool, crate or bucket. You need to let the entire length of fabric hang loosely without it touching the ground.
In this position, determine how long you'd like the skirt to be. Mark the position with water-soluble pen, chalk or a needle.
If you have a sewing bust, put the skirt on it and set it on the podest. (If you don't have one, ignore this step and let a second person help you with the next steps.)
Measure the distance between the ground and the mark. If you have a tool to help you, set it's height to this distance.
Move the ruler / tool around the skirt and create marks on the way until you marked all around. Be sure not to pull the fabric while marking the hem line.
It's always a good idea to pin the skirt to the new length and wear it again to see if you measured correctly before cutting.
Don't forget to add seam allowance to hem the skirt! If there is not enough length for allowance, consider the blind hem solution instead.
Cut the skirt at the mark + seam allowance and sew a new hem.
If you like the pink detail on the original hem, you can add it as a trim line by cleaning up (hemming) the cut edge and sewing it behind the hem you created (just a few millimeter lower so it peeks out under the hem line). Maybe it's just a pink cord you can remove from the original hem and apply to the new one.


If you prefer the blind hem, you'll have to adapt the measuring process:


Follow steps 1 - 3 above (mark the desired length of the skirt in one spot).
Measure the width of the original hem.
Adjust your marking tool to mark the skirt at desired length - original hem width (shorter than the first mark) and mark all around the skirt.
sew the seam line of the original hem to the mark you created, right sides together. Fold the rest of the fabric up and sew a blind hem:




The black line is your skirt, the loop is the original hem, the blue line is your mark and the green line is the blind stitch. First pin the seam of the original hem to your mark and sew right over the seam. Then iron then fabric up to reveal the original seam. Actually sewing the blind hem requires some more folding. You want to sew mainly on the excess fabric and only tiny stitches through the upper part of your skirt.
Basic tutorial for blind hem
Video: sew blind hem with sewing machine
Video: sew blind hem by hand

There are several pitfalls that await you in the process of measuring.


Wash, iron and/or hang the skirt before measuring. Cotton shrinks when first washed, so you want it to shrink before you shorten it. Wrinkles pull parts of the fabric together, which might result in an uneven hemline. If you cannot iron the skirt, let it hang freely from a sewing bust or a coat hanger to let the fabric reach it's natural form and length.
Measure from the ground up, not from the waist down. Your body is more flat in the front and more rounded at the sides and backside. Rounded parts require more fabric to reach the same length. If you measure the same length from waistline to hemline all the way around, you and up with a skirt that's too short in the back.
Wear the skirt while marking the new hem line.  If you measure while the skirt hangs on a cloth hanger, the hem will look different once you wear it (because of the shape of your body). 
Wear the shoes you prefer to wear while measuring. Wearing high heels requires a little more length in the back, while wearing flat shoes shortens the back line.
Stand on a podest so the fabric hangs free all around you. If some of the fabric lies on the ground, it props the parts above it up, while other parts hang down lower. This results in an uneven hemline.
Don't pull the fabric while marking it. The professional skirt hem markers blow powdered chalk onto the skirt to mark it without touching it. If you don't have one of them, you must be very careful not to pull the fabric while putting a needle in or drawing a line with chalk.