Our sun is a star. So everything touched on about stars apply to suns as well.
Twinkle Twinkle Little Star...
If you ever notice, astronomers talk about the "Celestial sphere", which is basically the illusion that all the stars in the sky (excluding the sun) all seem to be in a sphere that surrounds the Earth.
In using seem to be, I also note that the stars are actually of different distances from the Earth, and from different constellations at different points of the universe. This means that you should not use terms like <Insert Constellation name here> Sector. Also, don't try something like Lost in space's constellation finder (probably why it didn't work in the first place). Place names like Alpha Centauri Space may be possible though, for something referring to 2 light-years within Alpha Centauri.
The Earth's celestial sphere rotates just over once a day - once a day because the Earth is spinning, the just over because it orbits the Sun. The time just over is = length of the day divided by the length of the year.
One star, or a star system? You decide...
As I watched the two suns set in sequence, I had to squint my eyes to see three blazin' fireballs rise from the East. Oh, what else can go wrong.
A tip: Don't.
- Systems that have more than one sun have very great fluctuations in temperature. Little to no life can survive.
- You'll end up with the problem of fives:
- You'll need to be five times further away from one sun than the other.
- There are Lagrange Points where such bodies can exist, but the stable points require that the difference in the mass of the two suns has to be greater than 25 times. A red giant and a white dwarf? Not a good idea.
- There are other problems, such as the N-body problem
If you still insist, read this to figure out more: 
Note that there are very few planets found orbiting star systems. If a planet isn't in the right spot, one of three things can happen:
- It gets flung out of the system.
- It gets adjusted till it orbits properly.
- It gets swallowed by one of the stars.
One example of a planet orbiting a star system (with three stars) is HD_188753_Ab.
One thing to note is that star systems > two usually are combos of binaries + single stars, like this:
Typical three star system:
- Star A and B form a binary star system.
- Star C is another star.
- The AB binary system forms another binary star system with star C.
It has been noted that Earth-like planets in binary systems need the two stars to be seven AU apart, while the planet orbits one of the stars. It is not known whether planets can orbit two stars at once, as in the planet Tatooine in Star Wars, in which the stars were less than one AU apart.
Also note that in star systems like Alpha Centauri, one of the stars may prevent planets farther than a certain distance away from forming (much like how Jupiter does).
A single sun
Tat blazin' fireball in the sky, providin' life...
Now that's better. One sun simplifies things a lot.
First decide on the type of sun you want. A spectral type G2, like our Sun?
A graph shows that Luminosity = Mass^3.5 in solar units.
Properties to think about
But be creative
Ultimately, when writing creatively, you need not concern yourself with the limitations of science in the creation of your Conplanet. Consider Terry Pratchett’s very popular Discworld series in which the flat circle of Discworld rests atop the backs of four elephants riding an enormous turtle. There's plenty of room for mythological exploration and parody when Conplanet creating.
- http://www2.potsdam.edu/islamma/Phys335Ch08StarProp.htm : Right at the bottom of the above webpage, you have a nice chart of various properties of stars.
- http://www.kheper.net/cosmos/stars/stars.htm : Some interesting (and maybe useful) links on things like the properties of the nearest star and a star explorer.