Thats not such an easy question to answer. I have the same dilemma sometimes...do i train somewhat tired or get more rest and train then but risk getting into the habit of missing work-outs...
For me i'll just say this
1)training tired is the only time i really got injured in training
2)Now i try to think ahead of time and anticipate what is going on this way i can kind of adjust my training to fit my schedule REALISTICALLY. I hate to say it but if i know i won't have time to get to the gym to do squats or do a full work-out, I'll do tabatas(which i learned about here on this forum!) which only take 4 minutes that morning when i'm fresh.
3)try and stay relaxed through out the day (not that easy)and eat frequent small meals
4)Then again i got a friend who runs no matter fucking what and he's one of those people who claims the body can sustain/adapt to unbelievable stress and i've never heard of him being sick or injured
So basically my post was of no real help...good luck...
Sometimes, my body seems like it has just been destroyed. I feel beaten down and tired. This is a sign for me to take a day off. For instance, last saturday, I skipped my lifting and BJJ workouts that day and had 2 days off instead of 1.
Depends if your mentally tired after a long day at work or physcially tired.
If its mental, you won't ache as much but you just won't have any go in you. At such times I go. If everything hurts/aches, THEN have the day off because thats when doing the training will only make you worse. Its a thing to do, differentiate between the two though, I still have problems.
I'll say this though, after the warm up I'm ready to go if mentally tired and I'm always glad I went. Physically tired, I feel dead after 5 minutes skipping and it goes down hill form there