How can I colonize a system with no food production?

There are a variety of ways you can get food in systems like this; generally combining as many as possible is the way to go, given how important food is in Endless Space.

• Build food planetary exploitations on the planets
• Bring a leveled-up administrator hero with the +food abilities (and ideally +production as well)
• Focus on building (or buying) system improvements that will give you food on those planets
• Buyout terraforms on the first planet you settle to get it to a food-producing type, so that it can support the rest of the system
• Explore available moons & build the system improvement that gives +3 food per person on explored moons

The Colonial Base (that you get for free when colonizing a system) provides +2 food to start with so your initial colonists don't immediately starve. ^{From a comment by Raven Dreamer}

You can in fact specialize a barren or volcano world into farming -- it's just that they'll do a crap job of it compared to planets where things actually live, so you generally don't do so if you have a better option.

@oblivioussage's answer is correct on all counts; additionally, I see that three of those planets have exploitable moons. I'm not sure of the exact name of the tech but I'm positive there is one that generates food systemwide based on the number of moons...

You get one free improvement when colonizing a system, and it gives you two food (it's the thing that looks like a tent). You don't need to worry about your first population point starving to death.

Once you've colonized, just build your best Planetary Exploitation improvement for farming: the default Evolved Soils (+1 food per person), the easy-to-get Alien Grafting (+2 food per person), or the more-distant Hyper-Scale Farms (+3 food per person). That will get your system started; you can make it grow faster by building some of the system-wide food-generating improvements, or just resign yourself to growing slowly. As you invent those better Planetary Exploitations, your planets will upgrade automatically, so you don't need to think about it very hard.

If you use the +1 food Planetary Exploitation on every planet, you'll stall out after your second population point. If you use Alien Grafting or better on every planet, you'll eventually fill the whole system. Either way, you are quite definitely forced into building either Planetary Exploitations or System Improvements that generate food.