@mornview seems to be asking how to go from
1.125" threaded to
1.125" threadless....
Everyone else seems to be talking about going from 1" to 1.125", or vice-versa.
In any case, i'm bored at work, so here comes the "tutorials":
1.125" threaded to 1.125" threadless: buy a 1.125" threadless headset; you'll need the EC34 size, top and bottom cups. Buy a threadless fork with a steerer long enough for your headtube,your new headset's "stack height", your intended stem
**EDIT-DON'T FORGET TO BUY A 1.125" STEM!**, and however many spacers you intend to use. Remove the old fork, and do something creative with it, like make a toilet paper dispenser out of it or something. Knock out the old headset cups. Install the new cups, and install the new headset's crown race on the new fork. Mock everything up. Make sure you know exactly where you're cutting the steerer, and try your best to cut square. You'll want to cut it a few mm short of flush with the topcap, as it needs a gap in order to set preload correctly. 3mm or so is good. Install the starnut. Etc. Refer to the parktool for a professional, in-depth tutorial:
http://www.parktool.com/blog/repair-help/threadless-headset-service
Required reading on headset standards. FYI, both the threaded 1.125" and the "standard"/original 1.125" threadless are both going to be "EC34".
http://www.parktool.com/blog/repair-help/standardized-headset-identification-system
Running 1" set-ups on a frame designed for 1.125" set-ups:
Buy these reducers, in the 1 1/8" to 1" size:
http://problemsolversbike.com/products/headtube_reducers
Buy an ISO 1" headset
Buy a 1" fork, that will have enough steerer and threads to accont for your new headset's stack, plus the frame's headtube, plus 2mm add'l stack from the reducers.
1" threaded to 1.125" threadless:
Clancy gave good links for the bmx/Schwinn/old-school american size headtubes. Doing this is easy; i like to use the stock cups and the cheapest loose-ball headsets from NECO and Sunlite; oversized things like the FSA Hammer will NOT work at the lower race. The second link Clancy posted is more of the 32.5 (aka EC33) "bmx"-size headtube conversion; you typically cannot convert a ISO/JIS/"Mini" 1" frame to 1.125", without cutting out the headtube and welding a new one in. The headtube itself is too small, as far as the ID goes. Although they will be 30.0 mm at the ends where the cups press in, on most frames, the ID tends to become more narrow towards the middle of the headtube's length. Even if you find a frame with the headtube ID @ a straight 30mm top-to-bottom, ISO cups are too small to realistically mate with a 1.125" threadless headset's topcone, plus they're too narrow to accommodate a 1.125" steerer.
**EDIT: I should mention that you can buy adaptor headsets for your "BMX"/old-fashioned 1" frame....there's the Retro Ryder from Genuine Bicycle Parts (see RRB Member @rev106 and/or http://genuinebicycleproducts.com/parts.html -- scroll down to find the headset) and RRB @chattymatty sells some sealed bearing headsets that will make the conversion. In both cases, they take an existing, commercially available EC34-size headset, and turn down the cups on a lathe to meet EC34 specs. The Retro Rider fits Schwinn and Schwinn-spec frames, but will be loose in a Worksman or a Murray, maybe others. ChattyMatty will turn one down to your exact specs, if you want to take a micrometer to your frame's headtube and get him the exact figures you need.... http://ratrodbikes.com/forum/index....sealed-bearing-head-set-for-old-frames.95068/
1" threaded to 1" threadless is super easy; just follow the same basic steps as outlined above for the 1.125" threaded to 1.125" threadless, but with 1" parts.
Note: every instance above where i typed the word "buy", you can substitute the verbs "find", "steal", "borrow", "build from scratch", "trade", etc. But often times, buying stuff removes the guesswork.
HTH
-Rob