A word on exchange balances: it is NOT RECOMMENDED to keep your cryptocurrency assets on exchanges. There are countless documented cases of people who lost access to their funds, either because their account was disabled, or because legislation forbade the exchange operator to give access to users based on their geographical location. Some exchanges have been hacked in the past and will be hacked. It is RECOMMENDED that you use your own wallets, that you secure them properly (more below) and that you limit the cryptocurrency held in exchanges only to carry the business/transactions you have to, and for the most limited amount of time, to reduce exposure.
If you have a job, your employer may offer a 401k or 403b retirement plan as part of your benefits package. These accounts invest your money for retirement, but your investment options are limited to the choices provided by your employer and plan provider. If your employer doesn't offer a retirement plan, you can open an IRA on your own with your bank or brokerage company.
Once you are familiar with the concepts above, and know that you can (and eventually will) be influenced, you need to do some research on what projects you want to invest into. There are to date 1400+ cryptocurrency projects listed on coinmarketcap, a website that tracks projects, market value etc. This is a good start to understand market capitalisation, price of the cryptocurrency unit in what we understand when we begin (fiat currency i.e. dollars or anything else), total amount of assets in circulation etc.

While most online brokers do not offer international trading, some do. Nearly every broker supports trading American depositary receipts (ADRs), which offers US investors an easy, simple way to invest in foreign companies. However, if you want to buy physical shares of an international company, then you need to do your research. Interactive Brokers is the leader in this space but is built for professionals. For casual investing, both Fidelity and Charles Schwab offer international stock trading.

Warning: Only invest in cryptocurrency what you can afford to lose! Be prepared to lose everything. Expect high fluctuations. Do not put in there money that is vital for you whether it is paying for rent, utilities, loans, mortgages or necessary goods (food & medicines). See this as spending money on collaterals or nice to have: restaurant, books, travelling, cinema etc.
NerdWallet's ratings for brokers and robo-advisors are weighted averages of several categories, including investment selection, customer support, account fees, account minimum, trading costs and more. Our survey of brokers and robo-advisors includes the largest U.S. providers by assets under management, plus notable and/or emerging players in the industry. Factors we consider, depending on the category, include advisory fees, branch access, user-facing technology, customer service and mobile features. The stars represent ratings from poor (one star) to excellent (five stars). Ratings are rounded to the nearest half-star.
Brokers are either full-service or discount. Full-service brokers, as the name implies, give the full range of traditional brokerage services, including financial advice for retirement, healthcare and everything related to money. They usually only deal with higher-net-worth clients, and they can charge substantial fees, including a percent of your transactions, a percent of your assets they manage, and sometimes a yearly membership fee. It's common to see minimum account sizes of $25,000 and up at full-service brokerages. Still, traditional brokers justify their high fees by giving advice detailed to your needs.

Bernard Baruch, known as “The Lone Wolf of Wall Street,” owned his own seat on the New York Stock Exchange by age 30 and became of the country’s best known financiers by 1910. Mr. Baruch, while a master of his profession, had no illusions about the difficulties of successful stock market investing, saying, “The main purpose of the stock market is to make fools of as many men as possible.” According to Ken Little, author of 15 books on investing and personal finance topics, “If you are an individual investor in the stock market, you should know that the system stacks the deck in its favor.”

Bonus Stock Market Tip: Everything above is related to how best to invest actively - in other words buying and selling into companies that have been selected by you. But what if you don't have the time, money or inclination? What if the paragraphs above put you off? Perhaps you were looking for a simpler guide? The stock market for dummies perhaps?
Arbitraging can be very lucrative especially with Asian markets (South Korea for example) where cryptocurrencies are exchanged at premium rates, but due to the high volatility of the markets and the congestion on major cryptocurrencies (Bitcoin and Ethereum) it is becoming increasingly difficult to do arbitraging because of potential incurred losses. Add to this the fact that exchanges need a certain amount of confirmations before balances are made available for trading and it makes it quite risky at least for Bitcoin and Ethereum.
If there are any lessons to be learned from the American sub-prime mortgage crisis, the 2008 stock market crash (information here) and Wall Street bailout that followed - and there are lots of lessons - it is that borrowed money can be very dangerous in investments, even when it is being handled professionally. The failure of LTCM, Bear Stearns, Lehman Brothers, Northern Rock and many others shows just how precarious a business model can be with too much gearing.
The number of companies offering brokerage accounts has increased, including banks such as Ally Bank. Some brokerage companies provide a simplified version such as Robinhood where investors can buy and sell stocks, ETFs, options and cryptocurrency from a mobile app for free. Although Robinhood doesn't offer trade options for mutual funds or foreign stocks.

Insider trading: this is formally forbidden and punished in regular markets by stock exchanges organisations, but since crypto markets are unregulated, there is no way to apply any control here. Insider trading is when you have insider information about a project before anyone else or before the news hits the public, and you can thus acquire or sell a lot of cryptocurrency before the news break, allowing you to make huge profits, or to minimalise your losses.
Investor Protection: Along with wealthy and institutional investors, a very large number of small investors are also served by the stock market for their small amount of investments. These investors may have limited financial knowledge, and may not be fully aware of the pitfalls of investing in stocks and other listed instruments. The stock exchange must implement necessary measures to offer the necessary protection to such investors to shield them from financial loss and ensure customer trust.
Why I’m buying: Spell out what you find attractive about the company and the opportunity you see for the future. What are your expectations? What metrics matter most and what milestones will you use to judge the company’s progress? Catalog the potential pitfalls and mark which ones would be game-changers and which would be signs of a temporary setback.