How should I go about designing clothing for a teddy bear?
For a simple night dress, you can make a tube out of fabric which is just wide enough to go around the body of the bear, from just under the front legs down to as long as you like it.
Attach straps to go over the shoulders.
I would go for separate straps on the front and back, tied on the shoulder, for simplicity. If you want to make a once on never off you can also sew the straps in place.

Less simple but still rather basic is a T-shirt shaped item.
You will need flexible fabric, as the bear will not be able to move much to help you and it likely has a rather big head.
I would not close the shoulders. For a once on and leave, you can hand sew the shoulders by hand or finish off the shoulders and neck like baby clothing and use snaps to close (and re-open) it.

To make the patterns, take the measurements, cut the pieces out of paper and try them on the bear. That way you can adjust before even starting to cut the fabrics.

A simple jacket is made like that, tube for body and smaller tubes for arms, and 'cut' the front of the tube. 
It might be possible to get it on by moving the arms or even bending them (if just stuffed and not moving) but if that is not impossible you can sew (by hand) it in place.

There are patterns for dolls and stuffed animals clothing online, you could use some of that for inspiration and adjust the pattern parts to the measurements of your bear.

Run an internet search on these words and several collections pop-up:
-patterns for teddy bear clothes free-

Edit:
It looks like your bear has very flexible arms, the kind you can push through sleeves in T-shirt shaped clothing, and a relatively small head (compared to other teddies) so a regular T-shirt with a wide neck will already be possible.

To measure I would take a tape measure (or a bit of string which you put to the ruler later) just under its arms as well as just above its legs where the tummy seems to be on its biggest.
Unlike T-shirts for humans, for your little fellow you want the sleeves a bit forward, measure the difference between the distance over the back and the front, I guess it may be as much as 2/3 against 1/3.
For the size of the sleeves, measure on the lower end, where they are wider.
If the fabric is flexible, you can make the sleeves a bit narrower further up, but stiff fabrics will not let the paws through if the tube is narrow.

These same measurements will hold for your jacket. With a fellow as flexible as this, you can use almost any fabric, as long as you are happy to sew it. Just remember to make the sleeves wide enough for the paws.