First rule is to buy the best tack and long-term use stuff that you can afford (I am but a poor college student, so the best I can afford still isn't world class by a long shot
). It's cheaper to buy it once and have it last 10 years than to replace it every two years.
This works for me, but might not be right for everyone: I trailer my horses to the vet's office, rather than have the vet come to me. I only have 2 horses, and by quirks of fate their annuals come months apart (OK for me, 2 smaller bills instead of 1 big one...), so they go one at a time. My vet will do vaccines/coggins draws in the trailer, and my horses are OK with that. An office call costs a lot less than a farm call, at least in my area.
If possible, buy sawdust/bedding in bulk. It can be hard to find, a lot of sawmills contract out, but $30 for a 6.5 cubic yards is better than 3 cubic feet in a TSC bag. Buying hay during hay season helps too. Just like bathing suits cost less in the winter, when people don't swim, hay costs less when people don't feed as much of it. Replacing just the "business end" of shovels manure forks, etc. and putting new ends on the old handles can save money. Putting new buckets on wheelbarrows rather than buying the whole shebang new helps, too.
And, last but not least, always ask yourself, do I really, REALLY, need