Running is an attritional sport. The impact of striking the ground over and over again places stress on the body and the accumulation of this stress can lead to injuries. Let's discuss what happens when the inevitable happens and you find yourself injured, and what can be done to reduce your time spent on the sidelines.
The most important factor in reducing any injury is being aware of it as soon as it rears its head, and making the decision to stop running. Lots of injuries are not the result of a particular session, but rather the culmination of stress on a particular part of the body leading to an overload. We don't know what is going on beneath the surface, so all we have to go on are our pain receptors. Listen to them. If you catch it at the right time, you are already going a long way to snaring a lot of injuries and minimising their effect.
Once detected, the single best thing you can do is...absolutely nothing. Tempting as it may be, now is not the time to stretch it, to massage it, to throw the kitchen sink at it. Believe me, I've been there. But like with anything that has bubbled up to the surface, you don't get it to simmer by trying to push it back down. Doing nothing is like turning down the heat on the hob, it will enable the injury to do what it wants to do, which is inflame. You can try and apply ice to the area for 10 minutes at a time, which will offer pain relief and may help reduce inflammation time. But apart from that, refrain from doing anything that may well only serve to aggravate the injury further.
Take things one day at a time here. There's nothing wrong with heading out of the door to try a run. As long as you start slowly then you can observe the injury and if you begin to feel pain, you can stop with no real harm done. It's just not ready yet.
Once the acute phase of the injury is over (this could be anything from 2-7 days), then it's a question of how serious the injury is. If it's minor then you may be able to start light jogging as above. If it's more serious then you need to enter into a period of rehab. Now is the time you can begin to work on it, but don't overdo it. Nor should you assume that the area where you feel the injury is the exact location of the root cause. Any rehab you do such as strengthening or stretching should encompass the area beyond where you feel pain. For example if you have achilles pain then working on your calf will almost certainly assist with the rehab.
Of course if you are worried about your injury or it persists then you should consider consulting with a sports physio. I recommend checking beforehand that they have experience working with runners so that they are more likely to be familiar with the types of injuries that we get.