Understanding of Flight and Orbital Mechanics
It is important that our natives understand the basics of flight and orbiting. One of the main setbacks of making it to space in our history was this, and was a problem even after the successful development of liquid-propelled rocket technology. Take Robert Goddard and the Pendulum Fallacy, for example, in which he believed that the engines should be placed at the top of the rocket so that the rocket would hang like a pendulum. Another such example was difficulty rendezvousing with early Gemini tests because of a lack of understanding of orbital mechanics.
Computers (Bonus, probably not necessary)
They should at least be able to run simple automated sequences. Controlling everything by hand in the constricted environment of a space capsule is very difficult and requires too many people, which would just add weight. They don't even have to be able to do computations if the pilot is good at math. But just some basic automation that can run sequences.
Edit: Computers may actually be unnecessary, according to jwenting's comment.
Solid fuel won't cut it, unfortunately. Solid fuels are difficult to control and not as effective for their weight. Liquid fuel is very easy to produce, though. Simple electrolysis of water can produce hydrogen and oxygen, and this technique has been around since the 1700s. Ethanol and oxygen is another good propellant.
Some Sort of Strong Material
If we're going to be realistic, the ability to create steel or some other light and strong alloy is a make or break factor. This they could probably learn very quickly from studying a crashed enemy ship.
Means of Production
They must also be able to create many of these, and fast. Organized factories will be required for producing ships at a decent rate.
Life Support (Maybe)
Just the ability to replenish oxygen for an extended period of time, most likely from a pressurized tank.
Other Things to Consider
How big are these planets? It is not uncommon for terrestrial exoplanets to be much smaller than Earth and still in the habitable zone of their star.
What is the history of this civilization? Not every civilization should be expected to develop just like ours. They may have some accomplishments offset. Maybe they've developed spaceships before boats, or maybe they have large factories producing spears. (These are just exampled, I'm not saying they are valid.)
I think that the biggest setback is going to be computers. If your civilization already has computers, you're all good. But if not, you're probably not going to be able to learn how to make them by salvaging from destroyed enemy ships, because they aren't easy to understand without prior knowledge. They can probably learn to replicate the enemy ships' material fairly quickly, however, and they could probably also learn plenty about orbital mechanics from them as well.
Stealing enemy ships is likely not a possibility. If we are talking about realistic spacecraft, then the capsule and maybe a lander stage would be all that was left and it would be out of the question straight away. If it was more like a space plane, then the if they speak different languages they will not understand controls, and if there is a password then that's about the end of their adventures.
Overall, if the civilization has come into contact with another that can make these ships, then they should be able to learn from them much faster than they would figure things out on their own otherwise.