Magic requires roleplaying. A spell is not a knife to be used and discarded. This chapter contains no rules or dice rolls, and instead focusses on the fiction and roleplaying aspects of characters who can use magic.
Each character has a source of magic - what they think powers their magic. This is mostly a roleplaying device, though it can also play into conflicts with NPCs and in certain situations the GM may rule only particular flavours of magic effective.
Here are some examples for sources of magic:
Magic happens in the soul and mind of the caster, and requires concentration, but also something more that is not easily described. A sense of self, an inner journey, a connection to god, inspiration by the spirits - depending on your source, you would use different words.
Whatever the details, magic feels like being alive in a way few other things do. And it feels draining and the mental exhaustion of reaching your mana burnout limits leave you struggling. If you reach those limits, you are spent, really really spent. At the mana burnout limit, you will be barely able to focus, which is why casting any more magic becomes near impossible and dangerous.
While using magic without being at this limit, casting can be a rush, a thrill. This is pure energy pulsing through you and manifesting in the world. Magic is exhilarating. Every spell is like a mental workout - when your muscles burn but you feel just so good.
Magic in Fallen Empire is mostly subtle. As a general principle, magic will not create sights or sounds beyond its primary effect. In fact, most magic is entirely invisible to common people, one of the reasons there is so much mistrust towards witches and other magic users.
What a magic user actually does when casting a spell depends on his Source and personal preference. A priest will generally recite prayers from a holy book, a satanic demonist may make blood sacrifice and shout in unholy languages, a druid may touch the ground and spill some water from his waterskin, etc.
All traditions also have rapid, improvised forms. A priest can just mutter a quick prayer from memory, a wizard may unleash raw power without his usual hermetic items, etc.
In other words, constraining or muting a magic user does not inhibit his powers (but it can reduce his position - see Casting Spells).
In either case, onlookers will generally see that someone is using magic, even if they do not understand what exactly it is he is doing.