The explanation for spell research is on page 82 of the rules and magic book.
1) Adding a new spell (let's say they found a spellbook and want to get the spells from it into their own spellbook):
-First, look at the chart, for a first level spell, it will take 1 X 1d3 days.
-The player says how many days they will spend doing this, if you're me, you will alway say 3! If you're one of my players, you will say 2!
-The Referee now rolls secretly. They roll a 3.
-The player pays 10 sp per day, depending on how many they declared (so I would pay 30 sp, my player would pay 20).
-The Referee declares if they succeeded or not. So I would have succeeded (no matter what the roll, since I played it safe and went for the maximum time) but my player failed because he spent 2 days researching but it would have taken 3 to do it correctly.
All of the above assumes we are using a library worth 1,000 sp (because it's a 1st level spell). If we are not, then the time would be doubled (so I would need to research 6 days in order to be guaranteed a spell.)
Libraries and Laboratories are explained more on page 83.
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As far as spell acquisition, you can do whatever you want! I'm currently letting a bunch (all determined randomly) at first level, and then they can gain another at every odd level (again, randomly). If they want to learn a particular spell, then they have to research it or get it somewhere else.
I allowed one of my players to transcribe from a spellbook while riding in a carriage traveling across England, and I would also allow it on a ship.