I'm new to this kind of game completely. I can't understand how to use the dice. How many of what do I throw in a ranged attack?
Welcome to the hobby! If you take a look at the character sheet, it has a section called "Attributes & Skills". "Ranged Combat" is a "Skill" governed by the "Agility" Attribute (along with "Driving" and "Mobility"). Both Attributes and Skills have a Rating from A to D, which corresponds with a "Base Die" from d12 to d6. A character with a rating of "B" in "Agility" and "C" in "Ranged Combat would look like this...
Agility - - - - - - - - - - -B - - - D10
Ranged Combat - - - C - - - D8
If this character took a single shot with no modifiers, they would roll a D10 and a D8 together. A result of 6 or higher is one success. A result of 10 or higher is two successes (obviously only possible on the D10).
Let's make that roll!...
D10 = 7 (one success)
D8 = 3
That's a hit! You do your weapon's damage on the target.
If the weapon had a range of 5 and the target was 6 hexes away, that's medium range, which has a -1 penalty. Penalties are applied by stepping down dice to a lower die "size", starting with the highest sized die. In this example, the D10 becomes a D8 as that is one die size lower. Stepping up dice works the same but you do it to the smaller die size - e.g. making the D6 a D8. You step down a D6 by removing the die altogether but you always roll a minimum of one D6.
Single shot at medium range...
D8 = 6 (one success) - - - die was originally a D10 but changed to a D8 for the -1 penalty for medium range.
D8 = 6 (one success)
That's a hit, despite the shot being harder! And, it's a good hit because of the extra success, which can be used in various ways (see rules).
There are Ammo Dice you can roll too, for weapons that have a high rate of fire. Ammo Dice successes (6s) can be used for various things like causing Suppression, increasing damage, causing more hits, hitting adjacent targets, etc.(see rules).
I hope that's enough to get you started but please do read the Players Manual as it's all in there.
[Edited for a mistake]