Turning and tacking carpet where it meets vinyl flooring

If you don't want a visible transition strip, you could also put down a tack strip right at the transition point, attach the carpet to the strip and then trim/tuck the excess into the crevice between the tack strip and the tile edge.

Only real "difficult" bit is to ensure the carpet and tile height are even so the carpet fibers will effectively conceal the cut edge of the tile.

Here's a really good DIY thread

I'd recommend putting the tack strips in after the wall. That way you can put shoe molding over the edge. The one time I ever replaced carpet I cut it with a multitool knife blade and I didn't need any specialized tools to get the new carpet down.