bspec is simple... slow in fast out. just remember that.
you goto bspec icon instead of the aspec icon when entering in a race.
then it counts down, while doing so you can hit the buttons when they show up to turn things on or off, or differnt numbers.
each number is for a differnt speed or technique... for entering turns you will want to go slower so reduce speed (depends on track and car and tune and bspec skills)... to like 2 or 3 and then when going out of the turn raise it to 4 or 5 depends on the course etc.... some turns may not need a reduction in speed at all, and as your skills go up that may come apparent too.
enabling overtake will allow you to pass cars... however with a lower bspec score this may be hard to do. raise your bspec skills by training them (as in the FAQ) and you will be able to do it much better.
but overall you will want to enable OVERTAKE right away by pressing the button on the controler to do so (i dont remember the button, but should show it on the screen lower bottom screen).
the driver follows a LINE and with better course skills will race that line better, BUT when you have overtake ON, it wont really folllow that line very well, so you will want to dissable overtake from time to time. lets just say the driver takes better turns faster with overtake OFF, but you may still need to reduce the speed on some turns, regardless of overtake.
i usually turn overtake off once i pass the first place car (meaning im in first place) - that way he performs better and often gains a greater lead, but i still have to manage him depending on tracks (cause some tracks regardless of bspec skills require you to lower speeds on turns).
usually a faster car than the competition will overtake better, but most things people see first is your player bumping the front person when overtaking... this is common with lower bspec skills/points... raising the bspec skills will lower this happening, and it happens alot when you have speed 5 enabled, which is PUSH, and thats what it seems to mean, push the opponent.
ok, i hope you get that, now we goto the P option
P stands for PIT, and when enabled (look on screen or manual it should show you what button on the contoler to push, when enabled it will be orange (or whatever color that is, basically NOT WHITE (that goes for all options when enabled)

)
when enabled your driver will PIT next round or whenever it see's the pit comming up. usually your bspec driver will pit automatically when your tires turn orange, and will fuel up too while its doing so. you can do it manually whenever you want tho... if you dont refuel then it will just go like 10mph until you reach the pit, im not sure if it enabled the pit icon automatically IF you have no fuel, so remember that.
often you wont have to select the tires you want when pitting, it does it all automatically, unless you want to change them because you didnt choose the right ones before hand mabe.
so thats annother key to think about, choosing the right tires before racing... somtimes racing soft or extra soft racing tires work for 2 or 3 laps, but when you get tracks with more laps your going to want to choose your tires wisly... especially for endurance races.
this is where you want to know the drivetrain of your car and choose the right tires... lets give an example... a car with an MR drivetrain will require hard tires on the rear, and softer ones on the front, well we want to balance it out so do some testing, some tracks i can get away with mediums in front and extra hard in back, sometimes i need hard in front and extra hard in back, it reduces pits to use hard tires, but softer the tire the better performance you get sticking to the road etc.
but im not going to equip extra hard to front and back tires both, if i can use a softer tire in the front or back i will try and use it and see if it outlasts the other tires.
a rear wheel drive is simular config to the MR config, awd will probably require all tires being the same or simular.
etc... get the idea, choose wisly because when your tires turn orange on either side (or for the case of the F1, if one tire goes orange) you will enable the automatic pit function.. its automatic, so most of the time you have to THINK about what to equip... sometimes tuning your car will make tire wear more, so keep an eye out for that, like TOE in or out, will often cause more tire wear etc.
all Bspec cars should be tuned.... i say buy a race suspention and full LSD, those are the 100% best way to win... hell i can win any race against the same cars (even sometimes faster cars) with only those two enhancements and tuning them good... with no hp upgrades to my car i can usually always win, even with lower bspec points.
so a car tune is esential to winning or winning faster and better. (also tranny parts are good to upgrade too, faster accell and higher top speed will help, par course).
THEN we get into the R1 button.. the R1 button will bring up the back view of the bspec screen... this screen is all you really need to look at when bspec racing, so its very usefull... you dont get to see anything fancy but you can increase the speed at which the driver drives... by 3x.
so press overtake and raise the speed at which you drive, then press R1 then press and hold L1 and tap the right D-PAD button 3 times, that will incnrease the speed. then look at the map progress (pressing X button should show it if it doesnt by default) and slow the speed before turns, sometimes WELL before the turn (the driver needs time to slow down, especially with low bspec skill points (lets just say he is really dumb!)). then raise it out of the turns.. some turns dont need to be slowd down.
keep an eye out for the "OFF road" icon next to your car in the list, this will tell ya he went off the course, and THOSE are the turns you want to go very slow around, mabe 2 or 3 or sometimes slower, and if its not working right try lowering the speed way before that turn!
raiseing the bspec scores will help that out abit, so keep that training in mind, you have to train the driver! a score around 80 for each skill should be good enough for anyone to win almost any race with the right managing and car... so dont worry about raising the skills to 100... its often not worth it, and even lower scores can win alot of matches, just the harder ones will require more score points.
i hope this all helps alot!