Download this guide from Briggs & Stratton
Alternator replacement guide
It contains everything you need to know and towards the back has generic wiring diagrams for most set ups
If you get stuck came back & ask questions.
The more question the better.
If you work from that book then we all will have the same information which makes things easier for every one.
Now for safety sake do not connect the magneto wire till everything is connected and then check that no matter what you do, the kill wire never ever has any voltage on it .
If this happens in use the magneto modules ( coils ) will be fried and they are not a repairable part .