Suica for dummies (IC cards) - get a Suica card (or similar card depending on area, f.ex. in Sendai there's Icsca card) to make travelling a lot easier.
You can get point cards (frequent buyer card, etc) for some stores that let you collect points that you can redeem. Other stores have point cards that you charge with money and use as pseudo-bankcards, etc, so pay attention to the type before you choose to get a card. For major chain stores point cards are plastic cards that are scanned digitally, but smaller shops may still use the old system of point cards that are paper cards that the cashier physically stamps for you (typically you redeem it when you fill up the chart on the card with stamps).
(Cups & glasses, bowls & plates, cutlery & chopsticks, pots & pans, lunchboxes... paper plates, paper cups, cupcake forms, etc.)
100-yen-shops (100円ショップ), for example Daiso, Seria, Can Do. Do note that some of the shops (Daiso for example) do sell a few items that cost more than 100yen (such as 300yen), and in that case the price is listed on the item, this tends to be larger items, electronics, etc. In a 100yen shop, if there is no obvious price on the item, it costs 100yen (most items do).
Second-hand shops, for example Hard-off. You may be able to get better quality items there than at the 100-yen-shop for the same price, and the aesthetics and style of the items is likely to be different as well. See a list of the different shop types in the "Off" chain at the official website here. Book-Off sells second hand books, but may also sell videogames and other electronics as well as anime merch, etc, because they are often combined (a large Hard-Off store may have clothes, electronics, music instruments, kitchenware, etc).
In grocery stores, meat and pre-made meals (like sushi packs) often go on sale after a certain hour in the evening so try to buy soon-to-expire meat to save money. Of course, make sure to cook and eat it before it expires (read online if you're not knowledgeable about food safety). Vegetables and fruit can also be on sale when near expiring, so keep an eye out.
Supermarkets (japan-guide.com) - "Note that many supermarkets begin to mark down their unsold lunch items around 14:00 and their other prepared foods from around 19:00. Discounts start off at a modest 10 to 20 percent, but progressively increase until closing and may end up as high as 50 to 70 percent. Many supermarkets also discount fruits and vegetables that are either blemished, overripe or otherwise not fit for sale at full price."
Some snacks, like onigiri, you can buy cheaply at convenience stores. For regular meals it's not recommended neither for health or economical reasons. The plus-side is that most convenience stores in major cities are open 24/7.
Second-hand shops are great, see Hard-Off, etc. You can find both everyday clothes as well as formal or sportswear for good prices this way. At a large Hard-Off you may be able to find kimono and traditional sandals for very cheap prices.
There are specific shops for second-hand kimono as well, but the prices there will be higher than at a chain like Hard-Off (while maybe still cheaper than buying a brand new kimono).
To be continued. Last updated: August 20th 2019