A frequently asked question.  Here are 3 common ways:

If the PIC is not isolated from the power line, just connect the AC line
through a large resistor to one of the port pins.  Generally 2 5 or 10 M
resistors in series are used.  Using 2 resistors in series helps keep
high-voltage transisents from breaking down the resistor and damaging the
PIC.  Also, do not use the RA4 pin since it doesn't have a protection
diode to Vdd.  If that's the only pin left, add an external diode.

If the PIC is powered via a small line-frequency transformer, use a
resistor to the transformer secondary instead.  The phase shift through
the transformer is minimal.

Finally, an optoisolator with the input driven by half or full-wave
rectified AC line can be used.  This is the most exepensive way since it
needs an optocoupler, some diodes, and also a 2W resistor to limit the
current through the LED.

The resistor to port pin methods will make the pin read high when the AC
line is more positive than about 2.5V, and low when it is negative.  This
isn't too noticeable if the input is 120 or 240V but could be a major
error working from a transformer secondary.  If you need an exact
reading, likely a small capacitor could be added to delay the 1-0
transition to exactly the zero crossing.  Synthesize the 0-1 crossing by
delaying a nominal 1/2 cycle.

Now that some information about the line phase is input to the PIC, it's
still necessary to use it to trigger the triac at consistent phase times,
while at the same time receiving IR messages which aren't syncronized to
anything.  There are a lot of ways to do this.  One of the simpler ones
that uses the '84s resources would be to use interrupts for the
AC-related stuff.  The power line 1-0 transistion would cause a INT
interrupt.  This interrupt writes a starting value (related to the
desired brightness) to TMR0.  The TMR0 interrupt triggers the triac and
sets TMR0 to expire again 1/2 cycle later (since the sync is only on half
of the zero crossings).
These ISRs could be fast and infrequent enough that they don't too badly
affect software timing done to decode the IR.  Once the first INT
interrupt has occurred, it may be a good idea to disable further INT
interrupts until after the triac has triggered for the second time.  This
would prevent noise near the zero-crossing from causing repeated
interrupts.