I'd like to try Alchemy without reading any Internet guides about recipes. Is there any method or pattern to discovering recipes, or must you simply combine two/three ingredients at random and hope it works?

Examples of patterns I hope exist:
More rare ingredients do more exotic things.
Ingredients with similar base properties have similar other properties.
Ingredients from the same natural families have similar properties (ie: flowers, animal products, etc).

If it's truely random, than I don't see how I'll ever figure it out. Hopefully there are patterns.

Just try your way forward and you will eventually succeed. Trial and error my friend, trial and error.

There are some patterns. The mountain flowers restore your attributes, elemental salts are pretty obvious, but other than that, not really. Combing three randomly or tasting ingredients manually is effective enough for me.

Similar groups do not share similar effects (at least, not enough to come up with any reliable pattern). However, I will warn you that often times rare ingredients do share more exotic effects
I recommend you just grab every ingredient you see and just take a few minutes every once in a while to run through what you have and experiment. It may seem daunting, but it will go quickly enough.

The alchemy perk tree gives you the opportunity to discover all of the effects by eating the ingredient.

One things thats much too rare are the actual recipes
Alchemists have some you can buy and I've had the ocasional one turn up in loot (but they are less common than spell tomes)
You'd have thought they'd be pretty common, virtually every alchemy table should have a couple sitting nearby (with a lot of duplication of the most common ones)

What I do is choose two ingredients that have the same results. That way I know the potion will be successful. That usually uncovers other abilities of the ingredients.

When you find a new ingredient eat it. It will help you to start the alchemy. Another thing you may do is to seek for some recipes. NPC mages and Forsworn seems to have recipes very often in their inventory. Third thing is just to try different combinations and find out which of them works and which doesn't.

Eat ingredients and combine two or three that match up to get a decent potion in the process. That's how I find effects.

This. The recipes in the alchemy shops are great, except I've only come across a very few, and they were pretty common ones like resist fire or somesuch.

They should also have an Alchemist's Guide to Skyrim book, with a few volumes, scattered about as well. Collect all 5 (or 6 or 9 or whatever) volumes and you've got yourselves all the recipes... or a listing of ingredients and maybe 2 or 3 of their 4 uses. Something that the player can use if they put the effort into finding all the books... something that is more beneficial than just eating one of everything you see. The 4th use could remain unknown and something for you to discover with your actual alchemy creations yourself.

There is one such book, "Herbalist's Guide to Skyrim," located in some ruins to the east of Winterhold. It doesn't have everthing per se, but it has a few good recipes in it.

This is a great idea. Slower than three at a time, but at least I get something. Thanks for all the info.

I take common ingredient like flowers that I have a ton of and know their properties will make potion X. Then add a third ingredient that I have a lot of to see another effect.

Also once you eat some ingredients and collect some, look for the lit recipes when u open an alchemy table. If u have 3+ ingredients that 'restore health' or whatev....try combos of those. I've done health, damage health, and restore a bunch to unlock effects.

Remember that alchemy skill raises based on the value of a potion. So spamming health pots ain't the best way...

Spamming Damage Magicka Regen on the other hand...lots of common ingredients, and it will raise Alchemy like no other.

There is also at least one book that has several recipes along with useful tips for gathering the ingredients.

I do this, but I go one step further and add a third unknown ingredient to the mix. Having three ingredients significantly increases the chances that you will discover some new effects. You will get a potion from the first two ingredients so the most you will have wasted is the third ingredient.

Thanks for posting that...much better said than my post