How does any government "create" the currency in the first place?
Do the central banks just print some notes and offer it as a service? Say, Use our notes as an exchange medium
Currency in economics is just the notes and coins in circulation. These are minted and printed by government. In every country the institutional arrangement will be bit different. In some places central banks do the printing/minting of the currency in some others its done by mints or treasury departments. In US the printing of paper money is done by The Bureau of Engraving and Printing (BEP) and minting is done by the US Mint (see explainer in Investopedia). These agencies are nominally under the treasury department but in practice they create new currency when Fed orders it.
If you are interested in money more general not just currency (i.e. notes and coins) then in general money is created by Fed with help of private banks. The money is created whenever bank makes a loan as whenever a loan is issued a matching deposit is created with the money in it. This is done for a most part all electronically. The amount of loans private banks can issue depends on monetary policy of Fed, its regulations and how much reserves/base money it creates (if you are interesting in reading more on this you can have look at this BoE paper McLeay, Radia, and Thomas; 2014). Money is also created when Fed directly purchases some assets, for example when Fed purchases treasuries it is done with newly created money.
It is not enough to just say: "Use our notes as an exchange medium" in fact there are many examples of countries where people decided simply not to use official government issued money but decided to switch to some other money (this is known as currency substitution). For example, in Zimbabwe people substituted their local currency for dollar (such currency substitution is called dollarization) and in fact between years 2009-2015 even government of Zimbabwe decided to give up and declare dollar official legal tender.
In order for money to be used there must be some demand for it. The demand for money can be created by government requiring that all taxes be payed with its issued currency. Furthermore, in order for people to keep using the issued money they must also be able to perform the function of money reasonably well (i.e. be medium of exchange, unit of account and store of value). In Zimbabwe the problem was that due to hyperinflation money completely lost its store of value function and hence people decided to use dollar - but that's just one example.
Or, is it something like we own the land and other assets, we put it at a value of some X amount
Not anymore. Modern fiat money are not backed by anything of intrinsic value. In the past under gold standard money was backed by gold and ever further in past money was literary some commodity (it could be gold or other precious metals, but also shells, stones, coca, cigarettes, livestock etc.). In such systems money derived their value also from the intrinsic value of the asset (or more precisely commodity).
If you want to know about history of money then a good non-technical account is provided by Ferguson in Ascent of Money and more technical account can be found in Davies (2010). History of money.
