Step 1: Verify you truly need a 'special' (custom) thread and cannot use one of the standard sizes. There are many more standard sizes than just the typical hardware sizes you find at the store or in a hardware catalogue. Advantages of using standard sizes are that mating nuts/bolts, taps, dies, cutters, gages etc. are more likely to be readily available. Look in ASME B1.1 or a general resource such as efunda http://www.efunda.com/DesignStandards/screws/screwun.cfm or Machinery's Handbook. ("Table 3, Standard Series and Selected Combinations - Unified Screw Threads" page 1736 in the 27th Edition; page 1716 in the 26th Ed.; page 1498 in the 23rd Ed.)
Step 2: Some 'specials' are less special than others. Resources such as Machinery's Handbook give values for certain select 'special' combinations. Also check vendors catalogues for mating parts in the required thread, for instance many small adjuster screws with matching bosses are available in 1/4-80 or even 1/4-100 sizes.
Step 3: Correctly specify the required thread on the drawing/product documentation.
'Special' unified threads are not specified using the normal UN, UNC, UNF etc. which refer to classes of standard sizes. Instead 'special' unified threads using the standard tolerances but custom diameters and/or thread pitches are designated UNS.
Quote (ASME B1.1-2003 6.1):
...The thread series symbols for the UN thread form are ... and UNS for any other intermediate and larger size diameter-pitch combination having tolerances to unified formulation.
For such custom threads you must specify more than just the Nominal ID, pitch and class, see ASME B1.1.
Quote (ASME B1.1-2003):
6.4 Method of Designating UNS Threads
UNS threads are special combinations of diameter and pitch with tolerance to unified formulation. UNS threads have the basic form of designation set out above, supplemented always by the limits of size.
EXAMPLES: (a) ¼-20 UNS-3A MAJOR DIAMETER 0.2500 – 0.2428 PD 0.2229 – 0.2201 MAX. MINOR DIAMETER 0.205
(b) .495-20 UNS-3A MAJOR DIAMETER 0.4950 – 0.4869 PD 0.4625 – 0.4593 MAX. MINOR DIAMETER 0.441
(c) 1.200-10 UNS-2B MINOR DIAMETER 1.092 - 1.113 PD 1.1350 – 1.1432 MIN. MAJOR DIAMETER 1.200
Section 6.5 of ASME B1.1-2003 talks about threads with unified form but different tolerances as well as multiple start threads and special forms not covered by other thread specifications.
Step 4: Assuming standard Unified form & tolerance the following link will help you calculate the required diameter information. http://www.boltplanet.com/Un/un.asp?txtseries_page=UNS Thread diameters are at the bottom of the pop-up. As with anything (especially anything free) on the internet, for critical applications you should verify its accuracy.
Note: Dimensional information for the old No. 0000, No. 000 and No. 00 thread sizes may be found in Appendix V of ASME B18.6.3-2003.