TL;DR:

In the first instance, my belief is that a government would have to create their own brand of Bitcoin (i.e. a new version of the blockchain) and use that to trade against other currencies. This is a useful move because the government retains control over their currency (they set the mining rules) and they don't suffer a wealth drain in the process.

In more detail, once a country (our mythical Seashell Island from the earlier draft) has decided that it wants to adopt Bitcoin as it's local currency the following timeline is likely to come into play:

Research into Bitcoin

At this time the government will need to look into what benefits and drawbacks Bitcoin is likely to bring to their economy. Assuming that they currently have a weak currency, then adopting Bitcoin early could be seen as a smart move since it gives them lower cost of entry into the Bitcoin marketplace.

Among the obvious advantages that Bitcoin brings with it are:

resistance to counterfeiting

resistance to inflation

easier to track than cash for traditional transactions types (i.e. not including private sales of high value private keys)

Some of the drawbacks are:

economy becomes vulnerable to loss of electricity/networking (true of all electronic transactions at present)

banks have a reduced regulatory role since transactions become largely anonymous

increased potential for anonymous transactions to take place in large amounts

This last drawback is perhaps the most serious since it allows for a vast amount of money to be moved in and out of the country without the knowledge of the government. Admittedly, this happens in the present system although due to the large physical size of cash it usually requires laundering of some kind (conversion to something precious).

However, government resources are significant and it is very hard to remain anonymous for long. Over time detailed statistics analysing transactions could be used by the police to pinpoint individuals reusing Bitcoin addresses. This process is made much easier by the existence of tools like blockexplorer.com and should be seen as an improvement over the existing traceability processes.

Setting up the necessary processes/contracts to obtain some form of Bitcoin

By this stage the government researchers will likely have determined that there are only a few feasible options to get hold of bitcoins (note the lowercase here):

set up their own mining pool (initially paying for it in their own currency) - unlikely

create a suitable contract with a mining pool to buy a large quantity of bitcoins (without including their own soon to be worthless currency - unlikely

encourage their citizens to go forth and buy bitcoins themselves and slowly drain the local currency into foreign hands then pull the plug on it (not exactly above board) - unlikely

Using any of the above approaches at this stage requires a significant transfer of wealth from the country into bitcoins and is probably the hardest part to get right. The problem is that there is no central authority who can control the supply of bitcoins exposing the country to the influence of the market. In the case of Euros, the exchange rate of the participating currencies was fixed well in advance after significant negotiation. When the time came to switch over nobody lost out because all the old currency was replaced with the new, which could be printed at will by the central bank.

It could be argued (by @David Perry for one) that some kind of intermediate value-store could be used, such as gold or silver. However, this still requires all of the country's wealth to be slowly converted to this value-store which will raise eyebrows among those folks selling it in exchange for a soon to be worthless currency. I'd welcome further discussion on this.

There is a significant danger that the country could be declared bankrupt in it's own currency before it is able to complete the operation.

EDIT to cover the most likely path by a government:

This would permit a staged transition and essentially solves the value-store problem. The value of a Seashell would be fixed against their SeashellCoin equivalent (probably as 1:1). In my opinion, this is probably the most likely mechanism that a government could take. The government could decide upon their own inflation model, select a Version entry and then throw a supercomputer on the job for 5 minutes to generate a few million coins. Once that's done then they can take advantage of the blockchain approach and off they go.

Setting up the necessary legislation to make them legal tender locally

Once an adequate number of Bitcoins are, somehow, in the government coffers they can then make the announcement that all local debts can be paid in bitcoins and will be accepted by a court of law. This ratifies Bitcoins around the world (assuming the country is a recognised state) leading to a huge increase in the value of Bitcoins. It also opens the door to taxation in bitcoins which would largely operate in the same way as it did before.

Value Added Tax (VAT) (aka sales tax) would continue to be added to Bitcoin transactions by merchants who would then transfer the money to the government at regular intervals, overseen by accountants

Income tax would also stay the same

Accounts would have to be returned along with their transaction IDs to allow verification of truth

Standard statistical methods to detect fraud would remain (relies on most folks behaving themselves)

Managing the transition among the general population

Since it is the government driving this then they are likely to provide all necessary equipment to facilitate the transfer. This would include:

recommendations for mobile phone applications (probably not likely to make their own due to "backdoor" privacy concerns)

provision of Bitcoin Wallet Devices that offer tamperproof private keys and are essentially like smartphones for those that don't have mobile phones (see the original Fred)

provision of EPOS systems that are Bitcoin enabled

All of the above would probably occur via contracts with private companies.

Handled well, the transition to Bitcoin would be like introducing a new contactless payment system. They would still want to maintain a secure location for their bitcoins (most likely a government backed bank) and after a while it would just fade into the background.

Reaping the benefits to the economy afterwards

Much of the long term benefits would stem from

the decreased transaction friction within the existing legal and banking system

better fiscal policy since supply is limited leading to improved standards of living and quality of life

increased long term wealth as an early adopter to a global currency

greater transparency in accounting that can be easily verified

immunity to global currency crises

Just my 2 BTCs.