Privacy can mean different things to different people. What many people used to consider “private” is now shared quite freely with the entire world. The question is more then, “How can I keep the things I truly want private isolated from the things I want to share?” The options range from basic common sense up to elaborate isolation strategies.
Basic measures would be to not use common login names for different services, not using major hub services for logins (Facebook, Google, Discus, Twitter etc.), using ad blockers to prevent tracking and profile building (including denying most cookies) and various browser extensions designed to stop websites from setting tracking codes to follow you around.
Advanced measures bring us to fully cloaking your identity. The Tor browser is the most popular method for this. However, just using Tor browser alone will not truly mask you properly. One must “Torify” the other apps that may be running and enable them to use the proxy Tor provides to the system. Additionally, installing a very strict firewall/filter program (such as Little Snitch for Mac) will go a long way to suppressing extraneous communications that may publish your IP address or other data.
The Ultimate systems are “live os” images that are essentially single-use images. TailsOS is the best known of these. Every time it is booted, it is a fresh copy of the OS running plus all data is only sent over the Tor network.
On the crypto currency side, the first, easiest and most basic step is to not continually use the same address for all of your transactions. With modern wallet implementations, every address should be used only twice - once to receive funds, then once again to spend them. This prevents people from using the extremely easy method of just checking how much "balance" is available at your known address. Imagine if your bank card balance was continually published on the bank's website for all to see!
More sophisticated methods of obfuscating a "balance" of bitcoins involves shared coin transactions where the origins of coins become difficult to discern.
Where these two worlds (general Internet privacy & cryptocurrency privacy) come together is that one should be very careful when accessing one's coins if one is to keep the balances private. All it could take would be possibly collating browser fingerprints to connect your real world identity to an online wallet session.
Lastly, we consider the strict "Know Your Customer" (KYC) regulations put in place by practically a crypto/fiat exchanges.
One should never send funds to such exchanges directly from an address that carries the bulk of your funds, as the remainder of the funds would be provably belonging to you. Do you really want the exchange (who is beholden to regulators) to know the full extent of your holdings?
Financial privacy is the fastest eroding of our basic privacy rights in these days. It's up to you to hold onto this right using the best tools at hand.