Evaluating a Dominion Kingdom set
Know the difference between an early game card and a mid game card

Quickly evaluate what cards will be good for your first few buys (besides money). This is the only time where it doesn't matter if an action is terminal or not because you won't really have many actions. Deck thinning cards like chapel, cards that let you draw a lot like smithy, and cheap attack cards like militia can all be good investments. Plan your first few buys out of the good starter cards.

Other things to keep in mind:


Cards that give you +actions. This will help you judge how many combos to go for. If there's tons, stock up on those and draws to get some major combinations.
Cards that give you +buys. You definitely want a few of these for your later game, its a matter of what options you have. Don't go for woodcutter unless you don't really have any better choices. Having a good amount of buys can also help you end the game early if you want, but that requires some advanced planning.
Cards that give you +cards. How much money do I need to buy? Are cards that give +actions but NOT +cards going to be effective?
Cards that give you +$. If your only source of $ is from treasures, don't skimp on gold because your action chains will only get you more cards and maybe some attacks.
Attack and reaction cards. Helps you judge how much interaction there will be and how you will prepare. If there's going to be a cursing war (witch), might as well not get left out/defenseless.
How strong is big-money? This helps you know how hard you should go on actions. If all you need to win happens to be some silver, gold, a witch, and some counsel rooms, make sure you take that into account. Actually evaluating how strong this combo will be is more complex, but recognizing that it exists is a good start. 
Unique cards that need certain combos to work well. Don't get adventurer unless you have a higher density of gold in your deck. Only get gardens if you plan to have the cards to expand your deck to 40+ cards. Don't get a throne room unless you have something worth throne-rooming. Get a library or two if people are going hard on militia because it lets you redraw all the cards you lost.




As per your request, here's an analysis of the starting cards they recommend. 

Cellar, moat, village, militia, workshop, woodcutter, smithy, remodel, mine, market. They're listed here.

There's one strong attack card, so a moat or two would probably be a good investment if people end up buying as they should. Hit the village and market pretty hard (maybe cellar as well if you have a lot of weak cards in your deck) because they're the only ones that give +actions and you're main hope for getting big combos if you choose to go that route. Remodel and mine will let you get rid of bad cards, like estates, so get on that soon if possible. woodcutter and market both give +buys. Woodcutter is one of my least favorite cards as a silver is almost always a better bet. Since you can get +buys from market I personally wouldn't buy any Woodcutters at all. Village will be good for combos because there's a few terminal actions that are very useful (militia, smithy, workshop, etc.) Since remodel is available you will able to hone your deck to a slight degree later in the game, so don't be super afraid of buying cards that will only be mostly useful short-term, like a mine at the beginning of the game. 

for the beginning:


2-5 split: Get either a moat or a cellar for the 2$ buy and a mine. At this point, anything that gives you extra actions isn't really very beneficial, AKA village. Anything you can do to get rid of your bad cards (AKA mine) in the beginning is almost always a good idea. A moat will protect you from the early militias that will likely be played, but a cellar would help you go through your deck more quickly and get to the better cards in it. I'd probably go with the moat first and then cellar in the next few turns.
3-4 split: Get a workshop and a smithy/remodel/militia. These are all great early 4$ cards, the smithy will let you draw lots of cards, the remodel will let you trash bad cards, and the militia will put you ahead and slow others players down, all of which are amazing strategies. I'd probably go with the remodel or militia, but you'll be able to get more 4 cost cards with workshop soon after anyway, so it won't make a huge difference.


Here's some rough estimates of how many I'd go for long term.


cellar: 2-3, great cards that keeps your chain going. Good if you've only got 2$,  otherwise go with something more powerful.
moat: 1-3, Only get if militia is being used a lot, or maybe you need to draw cards for cheap, a cellar won't work, and you don't have many action cards (otherwise you'd probably have something better to play in your hand).
village: 2-3, good for mid game combos, depends on how many +cards cards you have.
militia: 1-3, beat on your opponents while getting money, what's not to like?
workshop: 1-2, good at the beginning, only buy 2 if you can remodel into market later or have a strategy that works with lots of cards costing 4 or less.
woodcutter: 0, go with a silver instead. This isn't a kingdom set where trading an action for a buy is going to be worthwhile very often.
smithy: 1, good at beginning of the game, maybe remodel later into gold. Only get 2 if you have a couple of villages or a big money strategy (not many actions in your deck).
remodel/mine: 1-2 of each. Try to get them early so you can upgrade your deck. Think about the odds of you getting them and the cards you want to upgrade at the same time. A mine is a total disadvantage if you have very little copper or silver, so plan accordingly. Remodel I'd probably go with 2 just because you can remodel gold into provinces in the later game.
market: 2-5. This is a pretty generic cards that is almost always helpful and will be strong with this kingdom set, but be sure to weigh it properly against the other options and don't just choose it because its a good all-around card. 
gold: buy lots early, there's not a set number. As I said earlier you will want to determine how much money you'll want to buy early in the game. Buy some silver early if you like, or use mine/workshop to get it instead. In the beginning you'll want to get gold whenever you have 6, especially since you can remodel them into provinces. Once you get to late game you might want to go with a duchy instead.


Potential combos: 


remodel + gold = make money into provinces during end-game.
remodel + workshop = get lots of cards costing 3-4 and crank them up to better stuff later. Workshop is a good early card that you can remodel later if you need to as its not very strong in the end-game.
remodel + mine = get 2 mines early and upgrade as many copper and silver as possible. Then remodel the mine into a gold once you don't need it anymore.
workshop + village = Use workshops to get lots of villages and smithy's while you use you actual money for better things. A village in your deck never hurts as long as you aren't using to much energy to buy it, and the village + smithy combination can get you some mega drawing action.
village + militia = launch a relentless attack with 3+ militias to keep other players' cards down. Add village to keep your chains going. If you buy up moats you can be even more evil.
cellar + moat + village = get some silver and gold
woodcutter + mine = get some woodcutters early with $ or a workshop. Use the extra buys to stock up on copper, and have 2 or 3 mines to crank up the copper into silver and gold. This is sort of a modification of big money, so getting a smithy can help. Just watch your number of terminal actions. I crossed this one out because its actually pretty weak. Buying copper is rarely useful, and relying on getting lucky to use a mine to upgrade it to a silver is pretty bad as it really dilutes your deck. 


These are only guidelines. Dominion is a dynamic enough game that no strategy should ever be followed to the letter. Use your judgement and knowledge of combos to make a good choice, but flexibility is always important. 

Another very interesting read is about the silver test, which is basically where you weigh all your $3, $4, and $5 choices against a silver. If you read this, be sure to skim through read the replies with +20 score to make sure you get both sides of the story! 



Evaluating a kingdom set properly takes practice, and experience is the best teacher. However, this should give you a pretty good start to learning some of the most important issues.

If you want to see some other specific sets analyzed, post them in a different question and I'd be glad to help. :)