So....alch rings. They are a tricky subject as there is quite a bit of randomness to their construction. Because of this, you could 'waste' many gems and much material trying to get the combination you are looking for. Lets start with how to create a ring. First, you will need a ring mould. These are available to purchase from the Alchemists Guild shop, and are fairly inexpensive. You will also need a gemstone, and some amount of material to use for the ring band. As an example lets say you have a ruby gem, a 50kg chunk of gold, and a ring mould. Make sure all these items are on the ground in the room with you and then:
cast mould ring at mould gem ruby material gold
If you successfully cast the spell, you should get a message similar to the following...

You are done with the chant.
You place some mineral and a gem in your mould and chant 'fingerrrr ovuuulah'
Using your expert knowledge in alchemy you mould a ring using 'gold' and a perfect dark red ruby!
You carefully extract the ring from a ring mould.
With your superior skill you manage to save a ring mould.
Ring powers: skill[find_weakness] 5 and avoid 1
Your item was good enough that you can name it and set its description.  The short description will
be suffixed with [Made by: ]
Enter the short description now: (max 60 characters, 1 line)
Starting editor (help: '~?').

As you can see from the above message, we managed to produce a ring that gives +5% to the 'find weakness' skill and +1 to our 'avoid' stat and the process has dumped us into the familiar editor. This first entry is a single line, the 'short description' of the ring, as shown in inventory. The next entry will be for the 'long description' of when you 'look at ring', and the final entry will be an optional single player's name, who is currently online (or link-dead), that will get added as a creator of the eq. This is nice because the namebonus can come into effect and grant higher bonuses than the 'base' effect that was reported at ring creation. More names can be added at the Alchemists Guild Guildmaster during this same boot for a small fee.

This covers how to actually make a ring, now onward to some more interesting stuff. Each gem/material combination will give differing results, that being said some gem/material combos can give the same results as a different combo, its all seemingly random as far as that goes. Each gem/material combination will give up to 3 different effects, although in my experience if you do get a 3rd effect on a ring its always -strength (for me anyway). Since this 3rd effect is less common, I'm going to discount it now and just talk about the first 2 effects, I'll call them the primary effect and the secondary effect. As you can see from the above ringmaking attempt the primary effect on this ring is 5% find weakness and the secondary effect is +1 avoid. The primary effect is always more potent than the secondary effect. Also each effect draws from a static pool of 3 different bonuses. For the sake of argument lets say that for the above combination of ruby gem and gold material your possible primary effects are skill bonus, int, and physical regeneration and that our secondary effects are avoid, charisma, and spell bonus.
After thinking on this some, here is an easier way to visualize it.
Pick one effect from column A, and one effect from column B.  This is what the ringmaking
procedure does for any given material/gem combination.

,-----------------------------.
| Column A     | Column B     |
|--------------+--------------|
| Strength     | SPR          |
| Intelligence | Avoid        |
| Wisdom       | Hit bonus    |
`-----------------------------'

Each ring you make can give 1 of 9 different results (3 primary effect * 3 secondary effect), although if a ring gives skill bonus or spell bonus that number drastically increases. This increase is due to the fact that instead of always giving the same skill or spell bonus, that particular effect grabs a random skill or spell to assign the bonus to the ring. In the above example, if you were looking to make a second 'find weakness' ring you could make 100 more rings, with the exact same combination and not get find weakness again, or it could crop up on the very next ring. So, as per Dryad's statement in her ring FAQ under "Are your rings reproducable?" she answers "Yes and no.". To perhaps make it easier to understand, lets take our imaginary ring recipe again but limit the choices to just stat bonuses rather than skill and spell bonuses. If your primary effect choices are strength, intelligence, wisdom, and our secondary effect choices are spell point regeneration, avoid and hit bonus, it makes Dryad's statement easier to understand. If you are looking to make a +wisdom ring you could end up making a relative handful of rings before you ended up with one with a wis stat. This method is much more reproducable than trying to go for a specific skill or spell.