Trainers - how do they work

How do the different levels of trainers work?

The documentation says "Only a level 5 trainer can take a skill all the way to the top. Each level of trainer can train higher than their predecessor, but at some stage, you'll need to employ the next level of trainer to continue improving player's skills" but does this mean that each level of trainer has a maximum level they can train to (and if so what is it?) or that higher level trainers can train faster (and if so approx how much faster) or both.

I am a complete newbie, so don't expect to have trainees of sufficiently high skill levels to need to upgrade my trainers immediately, but there is no harm in having the info to plan ahead.

Trainers do both, train faster and train higher. However, you can get incredibly high skills with most trainers. As your club finances increase and you get better facilities you will gravitate to better coaches, so you don't need to worry about it too much. Remember that a coach that is a higher level than your facility only operates at the facility's level, so don't go hiring coaches when your facilities haven't gone up as well.

That's useful to know. I will upgrade my training facility any worry about upgrading my trainers when I see how my finances are holding up.

Another important thing to remember is to 'not open' your new facility, unless you have have the same level coaches already in place. Each new level facility costs more to maintain, so there is no point opening a lvl 2 facility if you only have lvl 1 coaches.

While on this topic, what is better; to hire additional trainers to train existing squad or just buy new players?

You need to do both. You want enough trainers at the highest level your facility can use to train whatever skills you want for all your individual slots. In addition, when you can afford it you want to buy players that improve your 1st team, or who are exciting young prospects who can be trained up to replace 1st team. But with this later type of player, make ysure you have training slots available to give them.

"Each new level facility costs more to maintain, so there is no point opening a lvl 2 facility if you only have lvl 1 coaches."

So does this mean that the extra four training slots you get from a level 2 facility aren't in and of themselves sufficiently valuable to make it worth paying the extra maintenance?

I can see that you won't get enough slots at higher levels of training facility to make activation worthwhile unless you have good enough trainers, but I would have thought that those four extra slots for your first upgrade would be worthwhile, especially as they allow you to fully utilise four trainers ... or have I missed something blindingly obvious?

Horses for courses.
You will benefit from the extra facilites and will be able to use all your trainers 6 slots....
but the extra costs on the lvl2 will over the course of the season cost you 120k(i think) which is enough to get you 2 of the lvl 2 coaches.

Totally up to you tho.