When transferring from a room with a tiled floor to a room with a carpeted floor, you are undecidedly going to need a carpet transition piece to finish the job nicely. In my opinion, the best choice to use would be a metal transition from the range offered by Schluter Systems. Not only are their products of exceptional quality, they are also value for money if you are wiling to spend that little extra to complete your floor tiling project.
The carpet transition piece is basically a strip of formed metal available in a variety of different finishes suitable for your particular application, which gives a smooth transition from your tiled floor to a carpeted area. It has a flat cut-out face which slides in between your floor tiles and your subfloor into a fresh bed of mortar, and a smooth sloping visible face which hooks over the cut edge of a carpet.
To cut the transition piece, you can use an angle grinder with a steel cutting disc attached, or simply with a hand tool such as a junior hacksaw. With the power tool method it is a lot faster to cut, but if you are too heavy-handed with the angle grinder you can tend to scorch the metal blue due to it being of soft quality with the excess friction. The hacksaw method is just as effective and clean a cut, and will actually cut through the transition piece with ease because of its lightweight alloy composition.
Either way, whichever method you use will probably leave slow burrs on the cut edge, so you are going to also need a metal file to smooth down the sharp edges to give a near factory finish. When filing though, be very gentle in your technique. The metal is normally rather soft, so only file in one direction, pulling the file away from the end as you quickly stroke it, rather than using a back and forth motion. This way you can control easier what you wish to remove without overdoing it and maintaining a nice and even finish.
To mark the carpet transition piece for cutting, simply line it up against the door frame and mark with a pencil the size you wish to make it. Go slightly oversize though if you are not quite sure of an exact fit, as it's easier to remove that extra if need be in stages, other than the impossibility of trying to attach any back on.
When it is cut and ready to install, lay your final floor tiles firmly in place in a fresh bed of mortar at the doorway, align them with your tile grout spacers, slide the flat cut-out face of transition piece underneath the floor tiles into The wet mortar, and then double-check your floor tile alignment. By using the force applied to insert the transition piece butted hard up against the tile edges, you will probably find that the tiles have shifted since you laid them, so always check your alignment, and wipe off any visible mortar spots which may have squeezed out .
After a minimum period of 24 hours to allow for the floor tile mortar to completely dry, you can then insert the carpet into the transition piece. Cut your carpet to size and remove any excess overhang, but always leave a slight overhang wide enough to be fitted securely into the transition. Once trimmed to size, tuck the carpet under the protruding lip of the transition piece by hand, then push it in further with the use of a flat head screwdriver or your 6-in-1 tool, working your way along the full length.
If your carpet was cut to the correct size, then you will find that it will stay in there under the lip for good until the necessity arises to ever remove it. If it was cut too short however, and you found that you did have to stretch the carpet to tuck it in properly, then you may find in time that it will have a tension to pop out in due course. So, make sure you do not cut off to much that you had to stretch it to insert, and also do not leave it too long where it can create a loose carpet 'bubble' at your doorway, or point of transition wherever it May be in your room.