Attached are two rather crude schematics. Hopefully they will help you.
type 1 is probably like the Atlas switch where the points are separately wired from the frog, and wired to the running rails.
Type 2 is probably like the Old Pullman switch were the points and frog are one assembly and probably pick up power from the running rail the points touch. this is very typical of old HO switches for DC.
In either case, you need to change the polarity of the feed to the frog based on which way the points are thrown. You could do this with a powered switch machine that has contacts, or an SPDT manual switch. You could use a relay but then you also have to power the relay based on which way the points are thrown.
You only need SPDT (single pole, double throw) contacts for the track power. If want signal indications or feed back to a panel, you need additional contacts.
I have many manual switches on my layout that I throw with Caboose Industries ground throws. I have powered all my frogs. With manual track switches I use a small spring loaded SPDT electrical switch that has spring loaded arm. I used to get them at radio shack and they were about 3/4 inch by 1/2 inch by 3/16 inch thick. I mount SPDT so that the spring arm buts against the back of the throw bar when extended. Then when the throw bar moves against it the arm, it moves the contacts to the other setting.
I simply supply power to the SPDT from the running rails just beyond the point end of the switch.
For machine powered switches, there are usually SPDT contacts on the machine that change position when the machine is thrown.
If you want some photos of this setup contact me off list through my contact info.