1. You explain what you're trying to do.
2. You decide on how many shifts of power to use for the effect.
3. If it is less than or equal to your discipline, you don't need to roll to control the spell.
4. If you summon more than your discipline, then you have to roll and try to get high enough to match your shifts of power.
5. If you don't, you have to 'bleed off' the excess by either taking the strain or causing fallout.
6. No matter what, casting a spell causes a mental stress, plus one per shift of power over what I can safely draw with my discipline.
Mostly right. 3 is slightly off, you have to roll discipline to control any spell that isn't a Rote; a Rote which has power less than or equal to your discipline (+ specialties/foci). You have a number of Rotes equal to your Lore. As for 6, its pretty much right, except the cost can be covered by taking a consequence.
So from what I can tell, with a conviction of +4, I can only cast 4 spells within my threshold difficulty or one spell with +3 shifts of power before I'm out of the fight. That seems a little... weak? Any help on understanding this would be great, cause characters in the books can be using magic for significantly longer than just four actions before they're tapped out.
You can cast 4 spells, without taking consequences. If you are willing to take consequences, you could theoretically cast 7. One for each stress box, and one for each consequence level. The second bit is wrong, a spell with +3 shifts of power would fill your 4th stress box, but only your 4th stress box.
Do they? Dresden, at least in the early books, doesn't cast much magic per fight. A single spell (e.g, an attack) could actually be represented fluff wise as a 'flurry of fireballs', etc. As per the later books, at this point he's picked up Sponsored Magic. That allows him to take a point of debt, in exchange for what would have been 2 points worth of consequence (e.g, a mild consequence) thus allowing an extra spell per point of sponsored debt.
Another thing I am trying to understand is what kind of scale or scope does each shift of power mean. Does hitting someone with a five shift kinetic bolt hurt a lot? What about using a six shift spell to amplify my leap? How far does it throw me? or how fast could I go if i use a five shift speed/reflexes increase? How much could I lift... etc.
Depends on the table. Four shifts is Battlefield Weaponry: think C4, explosives etc, or high powered weaponry. So in my mind, 4 shifts is a fairly powerful spell. Harry's fuego and forzare start at this level. Many tables however see spells as high as 6 - 8 as Rotes at the Submerged level. A submerged Wizard of my creation will generally have 5-6 shift rotes - Harry's mentioned he's not exactly good at Evocation at this point, so those numbers seem reasonable to me. Carlos also wields 6 shift Rotes. A look at the write-ups in Our World might give you an idea: although many of the writeups seem underpowered, or are argued to be so by the majority.
Shift shift leap amp? First, see Harry's sidebar about Evocation based movement (aka, its a bad idea, due to lack of control). However a good ruling I've seen is 1 shift per zone, +1 shift per level of border that is in the way (although that was about blowing away an enemy, and was part of a manoeuvre).
The second spell? I'd rule that as block against attacks personally, but it depends upon your intent, as-to why you want/need the increase.
Also, a side question about intent and the first law of magic. If I were to use said bolt of kinetic force during a fight with a red court vamp and blew out a load bearing wall, bringing a building down on us but also crushing to death of the poor homeless guy hiding in the next room, did I break the first law?
Again, depends on the table. Some would argue that it still counts. Others that unless the Wizard knew about the homeless guy, he can't be held responsible, or have intended it to happen: thus no lawbreaker. The closest scenario in the books is the burning of Bianca's house, and possible civilian casualties. We'll never know if Harry gained a lawbreaker for that, as he already had one, and that would have only been a second strike (thus no increase).
Hope that helps.