Basically, you need at least 3 colours on your model. Typically an army has a main colour, an accent colour, and a detail colour. Some carefull planning will get you some great results.
Main Colours- Go with bright/dark distictive solids. The more traditional the better typically. ROYGBIV + Black and White is a good guideline, whith shades therein allowing flexibility. Some armies call for more dramatic colours, such as the Emperor's Children with their Pink armour. In such a case, try and make the accent a more traditional colour. That's why the EC have Black Trim.
Accent colours: You either want this to contrast in colour or in shade. Basically, you either want something like the Black and Pink of the Emperor's children (Colour) or something more subtle like a regal blue alongside enchanted blue (shade). Earthy tones tend to work better contrasted by shade rather than by colour, while radical tones tend to work better by colour.
Examples by Colour:
Red and Blue
Green and White
Pink and Black
Blue and Orange
Yellow and Red
Examples by Shade
Khaki and Brown
Blue and Navy
Yellow and Orange
Green and Forest Green
Avoid accenting with a light on light or dark on dark typically. On a miniature scale, it doesn't work as well.
Yellow on white/gold
Black on Navy
Pink on Yellow
Purple on Black
Detail colours: These are what you paint unit markings, eyes, weapon barrels, and other random details with. Try to tie together some of, but not all of, your detail colours. For instance, my blood angels have blue eyes in addition to blue carapace, which is their accent colour. Meanwhile their boltguns are metallic to set apart with a 3rd colour.
Some other things to consider:
1- Fluff/Required Colours: Saim Hann is Red, Ultramarines Blue. I paint you! Basically, your scheme is chosen for you (for the most part) if you are playing the actual fluff force. BUT that does not mean you can't add your own flourishes. For instance, my Blood Angels, while red, feature a blue carapace rather than the normal black. I link this together with blue eyes and power weapons rather than green. Any skull motifs I have I paint yellow and wings end up space wolves grey. When you look at it, it is a Blood Angel, but it is still a unique and vibrant scheme. Other armies are typically bound to a colour, but not as rigidly as a Space Marine Chapter. Orks are a fine example of this. If you are playing a certain warband (Goffs, Bad Moonz etc. etc.), they all have a specified colour, but you can choose contrasting colours and the amount in which to show their "official" colour.
Notice the Blue Carapace. It is not heavily present on the model, but is bright enough to jump out and contrast with the red, giving the model an even more visible tabletop presence. Black is another common BA colour, albiet not overwhelming shown but for in the Death Company. Thus I chose it for the chest conversion to futher bring out the piece, while binding it back to the model and army with the red blood droplet.
2- Unit markings: If you are trying to stick with an over arching scheme (Red for Khorne, or Black for Ulthwe), there are still ways to introduce colours to your force. Namely army and squad markings. I recommend both. If you look at the Blood Angel on the top right of the page you can see his squad marking on the right knee is different from the one above. Despite that, they both have an army marking on both their shoulders (a Black BA logo and a Yellow Blood Drop, Chapter and Company). Doing both can give you coherency in a squad and an army, but differentiate different squads. Markings don't always have to be a symbol either. A specific set of stripes, a sepereate accent colour on a helmet. Stuff like that. As far as unifying an army, I will turn to Eldar for an example. Often you want to paint a Aspect Warrior squad the colour of their temple, but you can link them to the army by including the colour of their craftworld. Black and White Banshees for instance on Ulthwe or Red and Green Scorpions on Saim Hann.