I have a lot of industries that are reporting, say, 50% transportation when I have trains waiting at their stations for their resource. What do I need to do to increase this percentage?
The % transported value reported by an industry is the % of its production of the relevant cargo last month that was placed in to any station - so it is the total of all its production placed in all stations (across all competitors).
If you have one station and are only transporting 50%, that tells me the station probably has rating at about 50% for that cargo type - in the case where there's only one station it, receives it's the maximum output multiplied by it's rating for each cargo. Note this cargo is placed in stations over the entire month (not in one go), so your rating at the end of a month won't match up exactly due to rating fluctuations over the month.
So, your first point of call should be to check and probably increase the collecting station's rating.
Station rating usually moves by at most ~0.78% (2/255ths) every 2.5 seconds, so it takes time to improve, as such the fastest method (but also temporary) to boost rating is an ad campaign, because it makes the rating jump immediately. The long term solution is to make sure there's as few goods waiting as possible and that there's no big time gaps between pickups as outside of ads and crashes these have the biggest impact.
There are a lot of factors to station rating, see so the wiki for full info on what effects what.
For me, it seems to work to have a bunch of smaller trains. So I'll have probably some 10 or so trains of length three (one or two loco's and four or five cars) that just go round and round :)
With that, I've gotten as high as ninety-something percent, but it's probably not very efficient.
Here's a sneaky way to boost station rating. I'm assuming you have enough capacity to take away most cargo generated; otherwise it may pile up and lower your rating anyway. You may have enough capacity but not enough frequency.
Build a road vehicle stop joined to your main station; bus or truck as needed for the type of cargo in question. Don't connect this to anything except a depot. If you use drive-through stops you can construct a small six-tile loop. Be sure your vehicle has a way to turn around, in any case, without needing to enter the depot. You may also use two joined stops.
Now buy one cheap vehicle; be sure to refit it to the cargo in question. Order it to stop only at this one station and 'Transfer and wait for full load'. The vehicle will repeatedly pick up and drop the same cargo. You'll get no income from this but your station rating will improve quickly and stay 'Very Good'. This will also help your Local Authority rating.