How you treat it depends on exactly where the character starts
Spirit Guardians interacts with the rules in an odd manner with respect to speed, going by RAW
Speed is defined as:
Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round. This number assumes short bursts of energetic movement in the midst of a life-threatening situation.
In the case of spirit guardians the effect states (emphasis mine):
An affected creature's speed is halved in the area, and when the creature enters the area for the first time on a turn or starts its turn there, it must make a Wisdom saving throw.
So while the character is in the area their speed is halved. So if a character normally has a speed of 30ft, and they start their move in the area, they have a speed of 15ft while in the area. The same is true of a creature that starts its turn outside the area, but moves into the area. While in the area their speed is halved.
Take this example:
- Character A: 30ft speed normally, starts turn 30ft away from the centre of the spell
- Character B: 30ft speed normally, starts turn inside the area, 5ft from the edge
- Character C: 30ft speed normally, starts turn in the centre of the area
Character A can spend 15ft of movement to get to the edge of the spell area, but as soon as they enter the area their speed is halved. By entering the area they will have spent 20ft of movement, but their speed is 15ft. As a result they can no longer move.
Character B, starts off with 15ft speed due to the spell. They can spend 5ft of movement to exit the area. Since they are no longer in the area their speed is no longer halved. As a result their speed is now 30ft again, they have only spent 5ft of it, so they have 25ft left to spend as they please.
Character C can spend 15ft of movement to get to the edge of the spell effect, but cannot leave it. As a result they have a speed of 15ft for the entirety of their turn and their movement ends when they get to the edge of the spell.
Some of this may seem a little absurd, but it's how the rules read.
Alternate solution, treat the spell's area as difficult terrain for a more consistent application
A more manageable way to treat this spell, as a DM, would be to rule the area in the spell counts as difficult terrain. In difficult terrain a creature must spend 10ft of their speed to move 5ft. This would make the time spent in the area consistently effect all characters, regardless of where in they start in respect to the centre of the spell.
For situations where the spell is overlapping with already difficult terrain, in order not to reduce the spells effectiveness, make sure to double the difficulty of the terrain within the spells area. So when the spell's area is on top of difficult terrain a creature would need to spend 4ft of speed to move 1ft. Rangers and Druids should also not likely be immune to this change from halving speed to difficult terrain. (Thanks to @PixelMaster and @MarkWells for pointing these two issues with the ruling out)
Best Answer
PH Page 190 has a section on different speeds that I think would apply:
Your Questions
You have a speed of 30 and move 15 feet. You then enter the area and you now have a move of 15 feet. Your already-traveled movement is subtracted from your move speed, which is 0 or less, so you can't use the "new" speed.
This is the opposite, you have a speed of 15, and move 15 feet and are out of the area. Your speed is now 30, and you've only used 15 feet, so have 15 more feet available.
Difficult Terrain
The section you are referring to is under the Speed heading, which states that "[t]he following rules determine how far a character or monster can move in a minute, an hour, or a day." Therefore, those rules wouldn't apply to in-combat movement since that has its own rules.
The rules for in-combat difficult terrain are found PH page 190:
Nothing about halved movement. Hence, I conclude that halved movement, at least in combat (since the spell in question has a duration of 10min, I don't see it being that useful outside of combat), means \$ \frac{speed}{2}\$.