Plug your guitar into your pedalboard and decide where the pickoff point will be, typically the last pre-amp pedal. From that pickoff point, route to input 1 on the Axe FX. On the grid, go IN 1 to AMP to CAB to OUT 3. Connect OUT 3 on the Axe FX to the input on the first post-amp pedal and then route the output of the last post-amp pedal to input 3 on the Axe FX. Back on the grid, separate from the prior blocks, go IN 3 to OUT X where X is your normal output to your FRFR/power amp/monitors/etc. As others have said, turn up OUT 3. You are now emulating a traditional pedalboard wired up 4CM to an amp, the only difference being you aren't emulating an actual FX loop on the amp (which is a good thing in my opinion).
If your pedalboard is something like a Helix or some other multi-fx, your routing options obviously increase. Just use the same layouts as above and remember that IN 1 on the Axe is the amp input, OUT 3 is the amp "send," and IN 3 is the amp "return." A helix, for example, the cabling would be Guitar to Helix Guitar In, Helix Send 1 to Axe In 1, Axe Out 3 to Helix Return 1, and Helix ¼" out to Axe In 3. You would have to route appropriately on the helix.
I have done this with my old pedalboard and it works great.