To help understand how it can be that you're flying 089 on your compass while flying on the 271 radial but tracking the 089 radial, consider this:
The VOR receiver doesn't really "think" in terms of numbers, it references 089 and 271 as two ends of the same line, with the station in the middle.
Without getting into details of how the transmitter works, let's say it's a polarity thing. "089" and "271" are just halves of the same line, as far as the receiver is concerned. It is fundamentally not a direction-finding instrument, believe it or not- it's a position-finding instrument. It's great for using in a homing mode, as a course waypoint, but that is not its true purpose.
The radials are just bearings. When the CDI says "TO" it means "BEARING TO", not "FLYING TO".
If you are on the 089 half of a line and the OBS is turned to show "TO" it tells you "okay; to know your bearing TO me, you need to look for the other half of this line you're on... keep turning the dial... there, it's 271." Ding! needle centers, and will now sense correctly, allowing you to fly to the station.
If you turn the OBS until it says "FROM", the receiver says "Okay; to know your bearing FROM me, you need to see the half of the line you are actually on... keep turning until you see... 271."
At no point does the receiver "know" your airplane heading, unlike an ADF. All it knows is the angle between you and it, relative to magnetic north.
This is part of how it figures "to" or "from"... if you have the OBS set on 271 but you are west of the station, unless you turned the OBS until it says "271- FROM", as in "BEARING FROM", it will sense falsely if you try to fly to the station.
But tracking 271 eastward to the station would be dumb... if you use "089- TO" that will more closely match your DG and compass, and if you are continuing beyond the staion, the CDI should just flip to "FROM" and you are all set to track outbound.
So in order for the CDI to sense correctly, you need to know what side you are on, which is simply a matter of knowing roughly which way the station is, in addition to which way you want to go.
If you're flying west, and want to use a VOR ahead to change course slightly but continue to the west from the VOR, you want to track a radial that's "on the west side", that is opposite your position (east of the station), but pointing in the direction you want to go (to the west).
Once you know this, when you select your radial with the OBS, you have to turn the dial not just for that radial #, but also for the correct "TO" or "FROM" indication.
-And it's not just for east/west/north/south... "TO/FROM" refers to a dividing line set 90 degrees in either direction of the radial you are on at the moment. Has nothing at all to do with which way you're going.
In other words, if you are flying a course heading of 352, planning to go straight to a VOR then change course to 053, you will track the 352 radial TO the station, wait for it to flip to TO as you pass overhead, then start turning towards 053 while dialing in "053-FROM" to set up for tracking that new radial.
You can see now why most airplanes with nav/comms have more than one VOR...
But it is very possible to work with one; I've done it many times.
