1. Paint armour panels Screamer Pink, the trims and metal parts Gunmetal metal (a Vallejo paint; GW equivalent is Ironbreaker I think). Adding in a few black armour panels can help create some contrast; look at Forgeworld's Word Bearers for examples.
2. Paint fleshy bits Rakarth Flesh.
3. Give everything (yes, everything) a wash with Nuln Oil.

That's pretty much everything for these guys, proper application of the Nuln oil should have turned the Screamer pink in a more crimson-y colour and made the metals look a bit more worn and dark. You can always highlight the edges with Runefang Steel for the metal bits, Eshin Grey for the black armour panels and Screamer Pink (or a lighter colour) for the 'crimson' armour panels.

Also, for the fleshy bits you can swap the Nuln Oil for a wash of your own choosing; Nuln Oil creates pale skin tones, Agrax Earthshade warmer ones, etc etc.

1. Paint armour panels Kantor Blue and the trims and metal parts Tinny Tin (Vallejo paint; GW equivalent is probably Brass Scorpion). Add some variety with black armour panels or painting certain metal parts Gunmetal Metal.
2. Paint tabards and scriptures (should your models have them) Rakarth flesh.
3. Layer Auric Armour Gold over the Tinny Tin parts.
4. Wash the gold with Agrax Eartshade.
5. Wash the tabards and scriptures with Nuln Oil. Agrax Earthshade can also be used, either in combination with Nuln Oil or as a replacement of it.

Again, highlights can be added at your discretion. I haven't found a good colour to highlight the blue with so far, if you happen to know something that can serve such purposes, let me know!

1. Paint armour panels Gunmetal Metal (Vallejo paint; GW equivalent is Ironbreaker) and trims and metal parts Tinny Tin (Vallejo paint; GW equivalent is Brass Scorpion I think). You can always add a few black armour panels for variety.
2. You can choose, either you try to freehand the hazard stripes now or you give the metal parts a wash first.

2a.If you pick the first option, carefully freehand the hazard strips with Auric Gold Armour. When painting on rounded bits (like shoulder pads), it's a good idea to try to first paint a single line as a reference for the others. Take some distance now and then while painting so you can check if your line is actually going straight across the rounded surface instead of accidentally curving upwards somewhere. You may need to give the gold more than one layer before the stripes are uniform.
2b. The other option is to give all the metal parts a wash of Agrax Eartshade (or Nuln Oil, Agrax Eartshade makes the metal look more worn though) first, and then take step 2a. Just remember that it's always harder to fix a 'washed' surface (should you slip with your gold while freehanding for example), as you'll have to re-wash the area you had to fix, which can create some colour difference.

You can wash the Tinny Tin bits here and there with Nuln Oil, to create some shading where there otherwise is none. Highlights can always be added, like Eshin Grey for the black armour panels or Runefang Steel for the metal armour panels.

Note before you begin:
Emperor's Children Marines are less standardized colour scheme-wise than their Traitor brethren, although pink and black armour panels will always form the baseline. It's up to you to decide which armour panels will be painted black and which ones pink, which can lead to some confusion while painting (for example, if you accidentally paint a panel pink when it was supposed to be black, or something along those lines). To avoid that to some extent, it's always a good idea to have at least a somewhat solid idea of what you want where.

Also, freehanding will play a bigger role here, mostly to paint flames on armour panels; if you haven't done this before, I suggest you look up examples online (like here on Dakka ) and do a few practice runs on a spare figure (if you don't have one, buy a box of 3 Space Marines (8 euros, damn you GW!), that should give you enough to work on). It isn't easy, especially not when you do it for the first time, but persevere and you'll be able to paint flames without breaking a sweat. They probably won't win any medals but anyone who expects you to paint miniature flames on miniature Space Marines absolutely perfectly deserves to get smacked in the face.

Now, on to the guide:
1. Paint the armour panels you want black Abaddon Black, and the ones you want to become pink Screamer Pink. DO NOT START FREEHANDING AT THIS POINT.
2. Paint metal parts Gunmetal Metal (Vallejo Paint; GW alternative is Ironbreaker) and fleshy bits Rakarth Flesh.
3. Wash the pink parts with Druchii Violet.
4. Layer Emperor's Children over the pink parts.
5. Wash the pink parts with Druchii Violet once again.
6. Wash the metal parts and the fleshy bits with Nuln Oil.

This is where I recommend you to start freehanding; the most common motif is that of flames.

7a. For pink flames, follow the same steps as you did for the armour panels: a base of Screamer Pink, a wash of Druchii Violet, a layer of Emperor's Children and another wash with Druchii Violet to top it off. These flames should go on black armour panels, but don't overdo it; one or two visible surfaces will do the trick.
7b. For black flames, simply use Abaddon black. You will need to be a bit more careful with these ones, as the pink you're painting on is a lot more difficult to fix than the black armour panels.

You can add highlights if you wish, I'd recommend Emperor's Children for the pink and Eshin Grey for the black.

1. Paint armour panels Death World Forest and metal parts Tinny Tin (Vallejo Paint; GW alternative is Brass Scorpion I think). Paint smaller details (like chains, skull icons, wires, etc.) Gunmetal Metal (Vallejo Paint; GW alternative is Ironbreaker) to add contrast and variety.
2. Paint fleshy parts and tabards/scriptures with Rakarth Flesh.
3. Wash the green armour panels with Agrax Eartshade. You can also apply this to the Tinny tin parts, but I chose to not do so for this model.
4. Wash the fleshy parts and tabards/scriptures with Nuln Oil (or Agrax Eartshade).

That about wraps it up for these guys. As always, you can add highlights where you see fit.

1. Paint all armour panels Abaddon Black, and paint/drybrush smaller metal details (mostly the joints of the legs and arms) Gunmetal Metal (Vallejo paint; GW alternative is Ironbreaker).
2. Paint metal trims and other parts Tinny Tin (Vallejo paint; GW alternative is Warplock Bronze). Paint one or two trims Gunmetal Metal (Vallejo paint; GW alternative is Ironbreaker) to add variety to the scheme.
3. Carefully apply edges highlights on all black armour panels with Eshin Grey. Remember to also apply them to the inside of the metal trims (like those on the shoulder pads; see example).
4. Wash Gunmetal Metal parts with Nuln Oil or Agrax Earthshade. You can also wash the Tinny Tin parts with Agrax Eartshade if you want; I only applied it sporadically on this model.