I am not new to The Elder Scrolls by any means.
I have noticed with Skyrim that if you have increased your skills enough, when you level up, YOU ARE FORCED to advance in level. You cannot stop at level 2, and then level up again when you are ready, even though you can save your perks.

So how do you NOT miss out on skill training, as they will only train you once per level?

If I wanted to skill train every level, does that mean I would have to level up, skill train, level up one more, skill train again, so so on?

If I am at level 1 right now, and I have enough skill increases to where the next time I level up, I will be at level 10, does this means I have missed out on 9 skill trainer sessions?

every time you level up you can train up to 5 skills (or 5 times the same skill if you want), so yea, level up, train, level up train.
skills that you use naturally level up when you use the related weapon/armor/skill, for example using bow will increase archery skill and so on, every time a skill increase also your level bar increase, so it's useful both train skills you use if you fell weak or train in skills you don't use for leveling up

I'm puzzled what your problem is...

By the by, you get 5 chances to buy skill training per level, not 1.

If you wish to skill train every level, then yes, you do need to level up, and then go buy more training.

Personally, as a newbie to TES/Skyrim, my problem (at low levels) was finding enough money to pay for 5 sessions of training, most of the time, practicising other skills provided increases & levelups before I could buy 5 training sessions

When you hit "level up" you get all accrued levels. You can't take them one at a time.

Yeah this is a problem for me too, its a really weird issue I think though

They took out attributes (strength etc) so people wouldn't freak about feeling they need the most efficient possible levelling, yet with keeping trainers the same issue arises, because *minor gameplay spoiler* so to be the most efficient you should use the trainer only for skills you aren't actively going to train but might use in a pinch (ie mage training in 2 handed) or skills you will never use, but you get the benefit of having the most possible level increases (and subsequent magic/health/fatigue increases)

honestly, I would take out trainers all together in the next one, they just seem to break the overall flow and levelling for me with little advantage to just having a properly balanced experience system

Correct.

you want to remain at level 1 but be trained to increase your skills and be overpowered against weak level 1 enemies...sorry but they don't let you cheap the game that way

The entire reason for people not taking their levels in Oblivion was because everything scaled with your level and people wanted to easy-mode level 1 content for the whole game. 90% of the scaling has been removed in Skyrim and what remains is more bracketed than proper scaling (certain mob variants don't appear until you're a given level). Remember that first Giant you met, that sent you into orbit? Yeah, he was level 32. So is every other Giant. And their pet Mammoths are level 38. Good luck killing them at level 1... even with exploits.

i killed a mammoth at lvl 2 with no exploits

After helgen i was wandering the plains near whiterun when I found a lone mammoth and i've wanted to kill 1 ever since seeing early pics..so i saved my game and charged in swinging; got stomped quickly. Reloaded and changed my tactics, i lured it to a small rock formation and proceded to stick and move like crazy, chipping away at the titans health, til finally he was almost dead. He took off running as i gave chase and wouldn't let my quarry escape but he stopped and stood his ground for the final showdown. I shot my 2 iron arrows into him and he charged, i ran past him nearly getting trampled as i quickly turned and finally finished my foe with 2 slices from my sword.
The epic battle was over and i reveled in my victory by eating his snout raw and keeping his tusk as a trophy

The problem with training and leveling in this game is that by training, you will gain levels. Then when you level up you are forced to advance several levels and you lose the 5 leveling opportunities of each level you advanced. Lame. The very first thing I did was to install a mod that allows 50 training sessions per level.

This is not good news.

Yes.

Too bad we can't skin them and take take their hides,it would save on chasing frikkin dear all over whiterun

My advice is not to use trainers at lower levels when you level up pretty quickly. Save them for higher levels when leveling is slower and if you haven't used much training it will still be relatively inexpensive and coin to pay for training won't be as much of a problem.

ha true 1 mammoth would provide all the leather you would need.
The dovakin is wasteful, he doesn't use everything from a kill and only takes 1...only 1 giants toe? He's got 9 more to give, falmer have 2 ears and mammoths 2 tusks. I don't understand your wasteful ways dovakin

Trainers? Never use them. If I decide to join the thieves guild, I might train lockpicking, but if you're patient, you can open even Master locks with relatively low skill.