Although investing in domestic stocks may seem intimidating, especially if you are a foreigner, it's very easy once you set up an account!
Known as a shouken-gaisha (証券会社) in Japanese, there are many, many brokerage accounts you can have access to in Japan. Functionally, they're all the same these days, although they might offer unique research tools. Each broker also has their own fee structure.
Signing up is usually fairly simple and can be done online. I went with Rakuten Securities since I'm deep in the Rakuten ecosystem and was approved without issue. These days browsers have automatic translation support which should help you even if your Japanese ability is limited. I'm happy with Rakuten, at first their interface takes some getting used to but once you know what every option does you can get all the information you need really quickly. They also have some excellent research tools, including the most recent four seasons report (四季報) for every stock,. Those are a great starting point when researching companies, as it gives an overview of the company's health and future plans along with historical numbers.
Interactive Brokers does have English support, and is probably a good option if you don't want to deal with Japanese interfaces. The only disadvantage is that they do not seem to have many research tools for the Japanese market.
I do not intend to have a comparison between brokers at the moment, fee structures and features can change and I'm not able to keep up with every single service! One thing that you might want to consider is for funding, if your brokerage is related to your bank then you can transfer funds without any fees, and there may also be some benefits for linking accounts.
Like I said, I was able to open an account effortlessly and from other's accounts it does not seem to be terribly strict to do so as a foreigner. However, Americans do have restrictions on some brokerage accounts and will not be able to buy non-Japanese stocks on most of them, although Interactive Brokers supports this. There are also PFIC rules which Americans have to worry about and thus should not invest in Japanese mutual funds, ETFs, and even some stocks (Orix and Softbank Group warn you about this on their English IR pages). This is beyond the scope of this site, but if you think that a company may be a PFIC then you can always email their IR department and they should be able to answer you.
Japan is unique in that stocks are sold in 'units' of 100 shares each, so if you want to buy anything you'll have to multiply the stock price by 100. This can make it challenging for those without much disposable income to invest, and I wonder if the high up-front investment encourages the perk system since you really have to commit to a company to buy into it.
Some brokerages let you buy partial units of individual shares, usually for a fee. Very few stocks have perks for amounts less than 100 (usually as the result of a reverse-split), and the share price takes the perk into account so if you do buy individual shares you'll be paying a premium for that. If you're aiming for the perks, expect to have to buy full units of 100 shares.
Fortunately, Japanese brokerage accounts have something called a 'tokutei-kouza' (特定口座) in which they take care of all the taxes for you. Dividends and gains from stock sales will be deducted by 20% for tax purposes and the rest you're free to use. You can choose to have a general account instead and do your own taxes, I'm not sure what the benefits would be but there are probably cases when it makes sense.
If you file your taxes online, the brokerage will provide you a file which you can attach and automatically do all of the calculations. This can be beneficial to get some money back from taxes on dividends, as they are technically double-taxed (taxed on company profits, and then taxed to you when you get them). Just upload the file and the online tax platform will do the rest for you!
This site is about perks and not dividends so I will not usually talk about them in the company pages unless a dividend is a defining feature of the company. There are a few things worth mentioning about them since you'll likely be receiving them in addition to the perks:
Dividend payouts are usually listed by share and not unit, so for most purchases you'll want to multiply the amount by multiples of 100 to get your expected payout.
Payouts are usually only once or twice a year, and the payout day is usually the same day that they mail your perks.
Since the payout day is several months after the rights day, you will often not know how much you are going to actually get. Many companies will list an estimated dividend payout schedule for the year or upcoming term and may stick to it, but it's also not uncommon for the actual payment to be higher or lower depending on the actual company performance. Some companies give no estimate so you're just going to have to look at historical payouts and estimate based on that.
You can choose how to receive the dividend. You can have it automatically put into your brokerage account, automatically transferred to your bank account, or get a physical check which you'll have to cash.
Getting information on Japanese stocks unsurprisingly requires some Japanese ability. However, these days browser translation functions are good enough that you can probably translate almost any webpage and understand what it is about. For .pdf and other downloadable files this may not work as well, although if you really want to read something you can always just copy the text and paste it into a translation site.
Your first step should probably be the company's IR (Investor Relations) page, some large companies even have a version in English and translate all of their press releases and quarterly reports. There are also a lot of investment-related websites although I've found that the kind of commentary you might find for American stocks is lacking here and most of the sites are somewhat dry, for better or for worse.
If you want some 3rd party information outside of official press releases, I typically read the 3 sites when researching a company:
Research tools that your brokerage provides. Each site will have different ones, but for example Rakuten lets me read the four seasons report, Nikkei Telecon, Barrons Digest, and Toushiru (which is run by Rakuten).
Minkabu - Your typical financial website, with the latest news stories that affect the market and the company pages have the usual data. One thing that's interesting is that it also gives a target stock price, separated into 3 categories. There's the AI target, which just puts the latest company numbers through an algorithm and spits out a stock price. It gives you the numbers and logic used to come up with the price, although it won't take into affect anything that's not hard data, so any future plans or sudden announcements which affect the business won't be considered. There's the community target where the users of the site can make predictions, I have not found these to be reliable and usually just ignore them. There's also the analyst target, which is the official target decided by reputable analysts, you can click through to get the number of predictions and the number for each one. Many smaller companies do not have any analyst interest so this may be blank. Minkabu will average all 3 targets to get a 'main' one, although since the community target can heavily skew this I wouldn't put much faith into the main target.
Yahoo Japan Finance - This site has the usual data for companies but I mostly just read this for the message boards which every stock has. There's a lot of people writing nonsense, but it can be useful to see how people interpret different press releases and company performance. I wouldn't necessarily make a decision based on what people write, but it's still interesting to read.
Some companies will also give a free subscription to their paid financial website as a stock perk (for example, JIA and SBI GAM), I own several of these and read them as well. The information can be interesting and there are reporters giving their opinions on the market, but a lot of the general reporting won't be too different from what you can read elsewhere.