How do I spawn fused TNT at a players location through the console?
You will use the execute command which will cause the command to run as though your friend is the one that executed it. With this, you will execute a summon command to produce the tnt at the player's feet.
execute <entity> ~ ~ ~ summon tnt ~ ~ ~ {Fuse:80}
Replace <entity> with the player's name.
If you want the tnt to detonate immediately, remove {Fuse:80} from the command. This specifies the number of ticks of delay before the tnt detonates. In this case, 80 ticks is about 4 seconds, which is the same delay that striking tnt with flint and steel has.