Spells

Spells are discussed in the FAQ at http://www.sjgames.com/gurps/faq/FAQ4-4.html#SS4.1.11
Under the base magic system you can't normally learn them by spending Character Points (since you can't use them at default) unless others around you are regularly using them.
Instead it uses the study-based rules to gain them.
==Changes that make the FAQ Out of Date==
GURPS Thaumatology changed a lot of things with regards to many aspects of the "base magic system" (if such a term even makes sense anymore). For example, Magery with limitations (and therefore enhancements) is part of the "base magic system" laid out in the Basic Set. Not only does Thaumatology effectively throw out how Dance Magery, Song Magery, Dark-Aspected Magery, Day-Aspected Magery, and Solitary Magery are described (changing the point costs of all of them) but it expands on the limitations and enchantments. With regards to Magery (Inspired Learning +20%) the FAQ is not longer correct as such mages don't need to worry about ferreting out obscure texts, hiring teachers, or any of the other related things true under the "standard" system. All that is required is a good relation with the power involved. Note, while this enhancement (along with several others) is built into Power InvestitureGURPS Thaumatology pg g7 if the Sanctity Replaces Mana enhancement/limitation isn't part of the package then it is still magery and part of the "base magic system".
Even within the now out of date basic set there is the Ritual Magic system where all spells do have defaults (as techniques not skills) and so can be learned. The one caveat to this the Ritual Magic skill itself must be learned from a teacherGURPS Thaumatology pg 125 Then there is Wildcard Magery, Magic!, and Wizardry! each of which are somewhere between the "base magic" and ritual magic systems.
Wild Talent is another approach. Syntactic Magic (which includes Symbol Magic) doesn't involve learning individual spells but rather words of the related Lexicon which are combined to cast spells.
==Bonuses==
All-Out Concentrate can give +1
*if using +1 for an optional Committed Concentrate then AOC would give +2. This is to balance ideas like AOA:ranged giving +2 to hit and Committed Attack (Ranged) giving +1, introduced in pyramid
Optional rule allows +1 for spending double the time on casting. This resembles Time Spent which normally you do NOT use for spells, though that could be an optional rule.
A bonus can be gained from the MoS of Symbol Drawing which has no restrictions against getting a 'time spent' bonus.
Magery can give a bonus.
P160 has Trading Fatigue for Effect which might be able to temporarily multiply magery. This is harder and not guaranteed, but has other benefits besides a bonus, if allowed (ie allowing stuff that requires higher levels, Magery and Effect limits)
P161 has Trading Fatigue for Skill which is purely for a one-time roll.
T39 has Trading Energy for Speed and Skill. This adapts Ceremonial Magic rules to standard spellcasting and is a LOT more expensive for spells with higher costs. It can be cheaper for small spells compared to TFOS though, since on a 1-energy spell spending 1 extra FP (+100% cost) gives a +4 bonus, whereas 4 FP would be needed to get that via TFFS. TFFS, if allowed, would be a better option for higher-cost spells though since +4 for 4 FP is a better deal for spells costing 5 FP and above.
Another major difference between these might be that TFFS energy doesn't come back in Very High Mana while TEFS does, and also that TEFS costs can be discounted for high skill while TFFs can't.
==References==