When you want to continue execution after the breakpoint fires, you have two possibilities: either the breakpoint was only supposed to fire once, or it was supposed to be persistent. If it was only supposed to fire once, you restore the original value you overwrote with your breakpoint instruction, manually adjust the address to that instruction's address (remember, regardless of what instruction was there, what executed was your single-byte breakpoint, so the adjustment is always trivial). Then you continue execution.
If it was supposed to be a persistent breakpoint, there's one added wrinkle: before you continue execution, you set the single-step (aka trap) bit in the flags on the stack. That means only the one instruction where the breakpoint was set will execute, then you'll get a breakpoint interrupt again. You respond to that by restoring the int 3 byte you had just patched to the first byte of the original instruction, and (again) continue execution.
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