Of course there are many variations on a theme, but the conventional route is that the acquiring company buys some or all of the shares in the company, which are typically valued based on some combination of metrics such as revenue and EBITA (which is a measure of the company's profitability). This is a really good reason for maximising income and minimising costs.
If the acquiring company is looking to control the company being acquired, then they will typically need to acquire 51% or more of the share capital (the total number of shares owned by the shareholders). This is important to understand as it is a mechanism for acquiring company to manage its risk - if things go well they can then go on to acquire the remaining shares, but if things go badly, they haven't had to pay for the whole company.
You asked whether it matters if the acquiring company isn't UK-based - in my experience it doesn't make a lot of odds (my UK-based firm was acquired by a Danish company), but there are some subtleties here; for example, you will typically want the acquisition to take place under UK law, which means they need to appoint UK lawyers if they don't have them already.
As per @edralph's points, when you get closer to that point, you will want very good professional support - you will need a good lawyer and a good accountant, preferably ones that have been through the process more than once before. Beware however, that this is a place where vultures circle - when some firms get a sniff of the money, they looked to maximise their slice of the pie.
In terms of preparing for such an occasion, it is vital that everything is 'in order' - this means your accounts need to be complete and up-to-date, and the rest of your admin is in order (especially client contracts and evidence that you own the intellectual property that belongs to the firm).
One piece of advice for nearer the time: if a firm wants to get into a serious discussion about an acquisition, then get them to put some money on the table. You can pretty much forget normal business once the process starts, and it can easily take 6 months, during which time you won't have time to go out and generate new revenue. This 'money on the table' can take the form of a kind of insurance policy - if the deal goes ahead, then they don't pay, but if the deal falls apart, at least you get some income in the door to cover lost opportunities.
Another small piece of advice for nearer the time: if at all humanly possible, try and be in a situation where you have more than one potential acquirer. The reason is simple: it's harder to set a market value for something when there is only one buyer.
Good luck in any case!