I have seen people over twitter asking if they should train if they are tired, so I thought I would give my opinion on this matter.
Personally, I have trained whilst being tired, but not so tired that I could have fallen asleep within a few seconds. Sometimes you will wake up, not having the best sleep, yawning a bit, and think 'ahh i'll skip the workout today'. That is when you should workout! Being a little tired is fine to train, it can actually be good because your body works harder as your a little fatigued. If you wake up and you can barely keep your eyes open, then you should obviously skip that workout.
How can you help this situation?
You need to make sure you get enough rest. Whether you're training for fat loss or muscle gain, your body needs rest to recover. If you don't get enough sleep (and quality of sleep) then you will wake up feeling tired which can lead to missing workouts. Try and make sure you get around 8 hours sleep, and good sleep! By that I mean - make sure you have a good mattress, try and relax your mind before you go to sleep (don't sit up playing video games or watching tv late at night, as this can affect sleep).
I have read articles about boxer's and cage fighters that train when they are tired, as they teach their bodies and minds to work when they don't feel like they can. This is an effective training method as its common that people give up when they think they are tired - when in fact your mind gives up when your body has much more to give.
Nutrition plays a vital role too! Make sure you're getting enough energy and protein from your diet and supplements - this will help your body to recover, therefore helping to take away tiredness.
So, should you train when you're tired? YES - but not if you are shattered, be smart about it!