There is a lot of good advice here. I'll pitch in my bit. I've thought about this a lot as I look at the 100s (maybe thousands by now) that I've spent.
There are two costs - gear, and ingredients.
Go all grain.
Grain, you pay what you need to... try to find a place that sells bulk 50# sacks. There is a malt factory in Great Falls, MT (I'm near Kalispell, MT), and my local homebrew supply store has gotten on thier delivery chain. When they get stocked I can get a bag for $38. Call around to all the places near by, one of them must have bulk grain. Consider your gas to go get it, team up with other brewers and maybe by 200-300# at a time if you need to.
Specialty grains often end up being a wash either online or in the LHBS. 10lbs at a time is sometimes cheaper.
Hops - again, buy bulk as well, it is way cheaper. 1 oz at a time is borderline robbery. The LHBS seems to again be a wash here when you figure in shipping. If you can buy a LOT of online with flat shipping sometimes it beats the LHBS, but remember who always has supplies for you locally - they need the business.
Yeast - start washing it. It isn't that hard, and will save you 3-5 bucks a batch. It'll also gives you a great yeast count to start with. It is the way to go, dive in and do it. Again, it's really not that hard.
Gear - If you want to keep it cheaper, consider being okay with smaller batch brewing. The cost (and complication) goes up exponentially the larger you go. At some point I figured I needed to do at least 10g batches - which is great and all, but it makes brew day longer, more expensive, and more complicated.
If you brew 2.5-3 gallon batches, you can probably do it all on your stove top with a much cheaper 5 gallon kettle, and a smaller cooler MT (or BIAB). 5-6 gallon batches are still kinda small, but tends to require a larger kettle, and also a separate more powerful burner that you probably have to use outside.
Chilling is also easier for small batch, as you can chill in the sink with an ice bath, or a simple immersion coil chiller if you want to invest in that. No need for a CFC or plate chiller and such.
In small batch you don't need a pump.
Keep it simple - herms and rims is neat and all that, but you don't need it to make great beer. Most of the pro's I know still make beer the old fashioned way with a big insulated mash tun and a single infusion.
I'm already geared up for bigger batch brewing, but if I knew what I know now, I might have been a little less zealous about gear, and focused more on the beer.
All great advice. By going all-grain, buying hops in bulk and reusing/harvesting yeast, many of my beers are $20 per 5G batch in ingredients, or even less. Hoppy beers and high ABV beers are usually more, due to higher cost of hops or malt. But a regular 5-6% Amber or Red Ale, or brown ale, saison etc. could be under $20 for 5-6G batch, which is less than 40 cents per pint.
Having said all that, and after thinking about how much less expensive homebrewing is (in ingredients) compared to buying beer at the store or at the bar, the biggest hidden cost is obviously time spent brewing/planning the brew day (recipe formulation, setup, buying ingredients etc), and also cleanup.
I now almost exclusively brew 10G batches instead of 5G, which cuts down a bit (it takes almost the same time to brew 10G as it does for 5G) - also allows me to split batches 2-4 ways and experiment with different additions, hops, yeasts etc., and I sometimes mash in late at night, go to bed and resume brewing in the morning - with electric heater pre-heating strike water while I sleep, so when I get up it's all ready to go. This saves me another hour or slightly more. Still, it takes 3-4 hours for my typical brewday.
Considering the time and effort invested, I am lately rethinking my strategy - for example, perhaps I should buy fresh hops and pay $2 or $2.50 or whatever per ounce, rather than use my year old (refrigerated and vacuum sealed of course) pack of bulk-purchased 1lb of hops which amounted to $1 per ounce, assuming I will finish it at some point before they go bad.
Similarly, I still re-use yeast, but I begin to think that saving $6.99 or whatever and risking some off-flavors due to poor yeast health in a beer that I only get to brew once every couple of weeks or so, may not be wise. I always do the starter, but still.
Malt is cheap, but again one can look for more fancy varieties, like Simpsons Golden Naked, or replacing your US 2-row in your malty beers with Maris Otter, and making saisons with Belgian Pilsner instead of US 2-row. This may almost double the malt price (I pay $1 per lb at my LHBS for US 2-row, and $0.80 if I buy it in bulk - 50lb bag for $40, while Maris Otter is $1.95 per lb), but it's a small price to pay for having an exceptionally tasty beer instead of just an average dull one.
I do water chemistry tweaks for all my beers now - starting with RO water (cost me $3.75 for 15G of RO water for 10-12G batches I usually brew nowadays, plus salts, could be another $1-2 per batch, plus my time of filling jugs with RO water at Glacier ), but I believe it's worth every cent. And let's not forget equipment which is a one-time expense (I had to chuckle while typing this - that's we tell our SHMBO's) but it all adds up as a hidden built-in cost of every batch. I like to keep things fairly simple but still, by brewing/kegging/serving setup has probably $2-3K of capital investment in it.
Over say 100 x 10G batches (equivalent to 200 5G batches), that's "only" $10-$15 per batch, but it still adds up. I suspect most people will never get to brew 200 batches (1,000 gallons) on their equipment - they will either never get there in the first place, or will switch to conicals and some other "upgrades" well before reaching this target.
Once you get to that level, saving a few bucks on a recipe while cutting corners is a bit like renovating your kitchen to make it into a chef's paradise, only to use it to microwave raman noodles, becase of desire to save costs per meal.
Having said all that, brewing can be (and is) a very, very inexpensive hobby.
In cooking a dinner, ingredients can be easily $5-10 per meal. In making mead, the ingredients are probably 4-5 times that of beer. (?)