There are a couple different ways (hypothetically).

First in photoshop. You take a photo, you fuck with the levels, the colors, etc. And you can add, combine, blend, etc more than one photo.

For these photos that is most likely how it was accomplished.

I can walk you through the process or even make a tutorial if you want more details. Look at the second photo. The artist is very skilled and you can see he took great case to blend the layers with the background (you can see the trees are actually slightly zoomed through each of the orbs, as if the orbs are a lens themselves). In the foreground you can see the colors on the ripples, mimicking the reflective properties of actual water. It isn't as simple as just making the orb semi transparent. It was probably a mixture of hand painting, blending modes, etc.

The first photo is done the same - same reflections in the water, on the ground. The reflections on the tree's leaves and tree trunks are a bit too exaggerated for my taste.

Hypothetically the same effect in photo 1 could be accomplished with light painting although it would be very very difficult, and still require a lot of photoshop work. I'm trying to figure out how you would successfully get the light to slowly change color like it does.

For this you just need a DSLR or SLR with ability to control how long the lens is open for. I've played with this technique and it is a lot of fun, but very difficult to get the proper effect. I was using an SLR for film school, so it was especially difficult because you couldn't do trial-and-error. You had to note your settings, go get your film developed, check them out, and try again.

The concept with light painting is that you have the lens which typically opens for a split second to capture the image. If you keep the lens open for longer, you can move very quickly and capture the movement in a single image. It works best with light in the dark because you need to open open the lens a tiny bit because as you capture the light from the foreground, you are capturing the same light over and over in the background. So if you do in during daylight, chances are you will quickly blow out the entire image. Wikipedia probably explains it better than me.

Things like this are just like any skill. You have to have the technical skills to make the program or camera or whatever do your bidding. At the same time, you have to have a mission and patience, and vision.