Hi
Firstly I assume you're using flexible track probably in OO scale?
The normal minimum radius I would recommend is equal to fixed curved track sections sold by Hornby or Peco and is to 438mm radius to centre line of track or also known as Radius 2. But many flexible track users will try and make their curves as large as is practicable and that will fit in the space available. So its not uncommon for a minimum radius to be 24" inches (approx. 609.6mm) Note all measurements are to the centre line of the track.
Simplest is to use a piece of string, a nail or pin and pencil. Position the nail at the centre of the curve and tie the string around the pencil at the distance out from the nail that's equal to the radius needed. Then draw a curve keeping the sting tight. Once a curved line is drawn pin track middle to that drawn curve.
A steel device call a Tracksetta is a useful tool and is sold in various pre set radius. I think 18" inches (457.2mm) is the smallest in the OO Tracksetta range. There are also Tracksetta for N gauge too. See Peco for details but all good model shops should sell them and eBay sellers too.
https://peco-uk.com/pages/tracksetta Using these ensures a constant curve (or straight) and the Setta has slots in it to allow pins to be inserted into the sleepers and baseboard to retain the track in place.
As for cutting rails then the best tool IMO is a Xuron rail cutter. Be cautious if purchasing one to obtain the correct type! The 2175B is a Top to Bottom cutter while the 2175M is a Side to Side rail cutter.
A Dermel type mini electric drill fitted with a metal slitting disc works well, but does not cut the rail squarely top to bottom as a Xuron cutter does! A Dermel cut is frequently at a slight angle due to the angle of the drill.
Finally a Razor saw can be used too.
I would also recommend obtaining a set of Needle files or at least a flat needle file to remove any slight burrs that all cutters tend to leave and that burr makes pushing the fishplate on harder.
Also on Peco flexible track you will have to remove the first sleepers rail chairs to allow the fishplate to slide on correctly.
