Cheryl, you are doing fine. Don't let the trainer stress you out. Are you still in school... or with a trainer on the road (an actual freight run?) There is a difference. The LATTER will yell at you and give you very little help. The FORMER should NEVER yell at you, as he is an "instructor" and you are there to learn.
I was "trained" (in school,) on older trucks. 8 speeds, 10 speeds and 13 speeds. They are ALL different. What are you driving?
My school provided a "chart" of sorts for which gear at which ROAD speed.... for each of the different trucks. You might try asking if they have one.
The rpm's will differ for the different tranny's (a little,) but I tend to go with the higher estimates here. Upshifting, you need to get above 15k for most tranny's in order to get the road speed up AND to be able to let the "load" off the tranny as you let up and "ease" the shifter into the gear which you should already have it positioned to "fall into." The reason shifting without the clutch is called "floating gears" is that once you get the rpms AND the road speed up to a certain level, letting off the gas will feel like "coasting" as you ease the shifter into the next gear. Works the same way using the clutch.
Don't "baby" the truck! If you're afraid to accelerate, you'll NEVER get the road speed OR rpm's up to a point where you can take "the load" off of the tranny! You cannot shift while the gears are "engaged" and under strain. As soon as you depress the clutch, the road speed will decrease faster than you can keep the rpm's up.
That's why GMAN said you needed MORE (higher) rpm's when downshifting. Because the weight of the truck/ momentum/ will keep going while the rpm's will drop quickly.
Also, as Roadhog mentioned, LISTEN to the tranny! You do need to "wind it out" a bit... but, don't overdo it. There's a point at which the truck will reach a road speed that is too high for that gear. The sound will "flatten out" and you will be "REV LIMITED." At this point, you can get locked into that gear and will have a hard time getting it OUT of gear let alone into the next one.
Double clutching is like doing the Texas Two-step. And as someone said.... you just need a couple of inches on the clutch. More like a "tap." So, technically... it is left foot, right hand (to neutral), then left foot, and right hand to next gear. But, it happens real quick with the left foot! In fact.... If rpm and road speed are synched perfectly... you can just single clutch. The next step is just "floating."
The reason you "grind" gears is that you let the rpms fall too quickly before you make the change with the right hand. This CAN be alleviated by keeping your foot on the accelerator and "maintaining" a certain rpm level.... or even slowly raising them to the level they should have BEEN at.
Like others said.... never try to force a gear. Put the shifter in the proper position [ and that means in LINE with the slot for it ] and then raise, lower, or maintain the rpm's at which it will just fall into place. [when going for the upper gears in each range, the ones to the far right, stick your elbow out like a chicken wing and make sure you get the shifter OVER to that slot!]
Ever hear that great country/folk/rock song by my favorite group (that I can't remember right now).... "Take a load off Annie!" Well.... that's the trick! You gotta get it up to a speed that you can "take the load off the Tranny!" And that load will differ between an empty trailer (in a training situation especially) and a loaded one! Then "two-step" it into the next gear before you lose the feeling!
Don't be afraid to DANCE! The truck already KNOWS the steps! If you hesitate... you will only step on her toes!
Good luck and keep us posted!