1. You must pay VAT at the first port of call in the EU. The value for calculating the tax will be negotiable in some places but your purchase invoice will be a minimum value! If you do this in the UK, Customs and Excise will include any shipping costs included in getting the boat here and any alterations / enhancements you have made since purchase. Ouch!
I cannot say whether you could reclaim any state sales tax levied in the USA on purchase, based on exporting a used vessel within a set time - logically you should have this benefit if the boat is truly removed from the USA. If you buy a new boat and have it shipped out, you will escape USA state sales tax.
If you are an EU national you will have great difficulty in persuading the authorities you only intend to bring the boat to the EU for upto 18 months before re-exporting it. With EU passports you face almost inevitable trouble from customs and excise authorities almost anywhere in the EU - not good for peaceful sailing!
2. The vessel must be certified under the EU Recreational Craft Directive which came into force in June 1998. A number of boats now made in the USA are certified as meeeting the standard, so no problems. If you chose one that predates the RCD or is a make not manufacturer-certified, you face difficulties. A new vessel imported must be certified and the cost of getting it certified is probabaly non-economic. There are few certifiers and the tests are frankly, nothing less than a restraint on trade! The RYA can supply you with all the details. If not certified, you would not be able to sell it in the EU other than on a knock-down black market basis.
As well as VAT you will also be liable for import duty in the UK.
As Peter says, beware of buying a US yacht that isn't EC marked. That means pretty well anything more than 5 years old. However, some older yachts will be exempt from RCD requirements if either (i) it was a originally built in the EU, or (ii) it was kept in the EU at any time prior to June 1998. You must have documentary proof of this - bill of sale, moorings receipt etc. There are a few other exemptions, but unlikely to apply.
To bring a yacht into the EU under temporary importation relief (Peter's 18 month point) you first must give up residency in the UK. This exempts you from UK tax, but also you lose NHS and some statutory pension rights. You first have to live out of the EU for a minimum of 6 months, then convince IR that it is long-term. To avoid some (but not all) of the additional hassle from EU authorities when you return, ideally the yacht should be registered outside the EU. USA won't permit forigners to register there, try Guernsey or Gibraltar.
Otherwise, without paying VAT and getting the yacht CE-marked you can't bring it into the EU at all, though in practice very short visits to the UK (under 2 months) under 'sailaway' arrangements would probably be tolerated.