The first thing you need to know about training with an injury is, you are the only one who knows your body. Never (and I mean never) let anyone else push you if you are injured. If there is a coach, personal trainer, sensei, or friend that tries to force you to train injured find another person to train with. There are several steps that you need to take if faced with an injury:
1. Assess the severity of the injury. Did you pull something? Break a bone? Is there swelling, bruising, or bleeding?
2. Decide if you need to discontinue the workout or just take a break. If you do continue, back off using the affected area.
3. If the injury is bad enough go to the hospital or schedule a doctor appointment. Never be too proud or act "tough".
4. If the injury does not seem bad remember RICE (rest, ice, compression, elevation).
If you are able to continue training with the injury make sure that you train smart. Do not over work the affected area. While you are training find ways to train muscle groups that will not stress the injured area. There are many ways to get a great workout without using the injured area. For example, if you have shin splints from running take time to go swimming. You can always find something, get creative.
Finally, if you are recovering from an injury train smart. Take time to rebuild and rehab the injured area. Find someone that is experienced in rehabilitation and take it slow. Make sure you have correct form and don't push your body too hard too fast.
Now take care of yourself and train smart.