To fully understand how to use Chapel, you have to examine its use with many different Kingdom setups. I will only detail some scenarios from the base game.
Standard Big Money Strategy
The standard Big Money Canonical strategy is to buy a Provence, else buy a Gold, else buy a Silver. To get a better understanding on how Chapel works effectively, it might be best to remove all the other complications from the deck, and examine how Chapel works to enhance the basic Big Money strategy. The first two turns will be Chapel and Silver. What are the possible 3rd/4th turns, that contain a Chapel? The table below shows the probability of getting a Chapel (Row) with different distributions of Copper (C), Silver (S), or Estate (E). Your other hand (Column), and its dollar worth are also displayed. (There is a 1/6th chance that you don't get Chapel until your 5th turn). These figures agree with my calculations, so I hope that means I didn't make any mistake.
|4C,S | 5C |3C,S,1E|4C,1E|2C,2E,S|3C,2E|1C,3E,S|2C,3E|
( 8.84%) 4C | - | - | 1.26% | - | 3.79% |1.26%| 1.26% |1.26%|(Trash4)
( 8.84%) 3C,S | - | - | - |1.26%| - |5.05%| - |2.53%|(Trash3)
(26.52%) 3C,1E |1.26%| - | 10.1% |2.53%| 7.58% |5.05%| - | - |(Trash4)
(15.91%) 2C,2E |3.79%|0.78%| 7.58% |3.79%| - | - | - | - |(Trash4)
(15.91%) 2C,S,1E | - |0.78%| - |7.58%| - |7.58%| - | - |(Trash3)
( 5.30%) 1C,S,2E | - |3.79%| - |1.52%| - | - | - | - |(Trash3)
( 1.77%) 1C,3E |0.51%|1.26%| - | - | - | - | - | - |(Trash4)
( 0.25%) S,3E | - |0.25%| - | - | - | - | - | - |(Trash3)
|5.5% | 25.7% | 28% | 20% | 3.8%| 16.7% |
| Turn 5|
If you compare the results of the Chapel Canonical is a deck of usually 10-9 cards, with a small 16.7% chance of not having drawn Chapel until Turn 5 (To mitigate this, it might be worth it to buy a Chapel during Turn 3 when you only have a $2 hand. I haven't worked out the exact math, but it looks like there is a ~0.8% chance that you draw Chapel 5th turn and only had a $2 Turn 3 hand, compared to a ~2% chance of having a $2 Turn 3 and drawing Chapel Turn 4. I think it is worth the risk of buying Chapel Turn 3 on a $2 hand to mitigate a slow Turn 5 Chapel Start. It is unlikely that you draw 2 Chapels Turn 5, so you should be able to shrink your deck by Turn 7-8 with the extra Chapel).
On Turn 5, the deck will usually consist of 2 Silver, 2 Estates (23% chance of Trashing 2), 4-5 Copper, and your Chapel. A Big Money Canonical deck will usually have 14 cards. It will consist of 4 Silvers (~28% chance of 1 Gold in place), 3 Estates, and 7 Copper. The most important goal for both of these decks is to hit that magical $6 hand. Starting with Turn 5/6, the Chapel deck should be able to pull this off more often. The Chapel deck should be able to buy a Gold during Turn 5/6, and should be able to remove another 4-2 cards. This will setup their Turn 7/8 with a 8-7 card deck that consists of 1 Gold, 2 Silver, 1-0 Estate, 4-3 Copper. From that point onward, the Chapel deck should consistently be able to buy Gold, if not a Provence. Big Money on the other hand keeps increasing the size of their deck. They draw their own Gold less often, and have a much higher chance of drawing the Gold with Estates (making it difficult to hit $6 or $8). It is important to note that by Chapeling away your Estates, you are 3 Points down from your opponent. It is vitally important to modify this canonical simplistic strategy to take into account the number of Provinces left, the current VP deficit, and which other Kingdom cards are available.
Thief (Treasure Stealers)
A Chapel strategy is very risky with Thief available in the Kingdom cards. Removing the chaff from your deck increases the likelihood that your opponent hits your Gold/Silver. This is especially true in mulitplayer where you will be subject to multiple attacks.
Workshop and Gardens (Quick Piles)
Ignore your Chapel strategy, it is too slow. Your opponents will increase the size of their decks making their Gardens worth 2-3VP, and will end the game on piles before you get your money building Province buying engine online.
Militia (Hand Destruction)
Chapel works because of its ability to remove chaff from a hand with Chapel in it. Any card that shrinks your hand size reduces the effectiveness of Chapel, reducing the trashing from a maximum of 4 to 2. A Chapel strategy gets considerably weaker in multiplayer, with multiple opponents able to attack you.
In general, it is preferable to not Chapel if you have another action card in your hand that would gain you a Gold/Province if you played it. Your first two turns will likely be Chapel/Silver, unless a really good $4/$3 card is available (Militia in a 2-Player game is very good, and shouldn't hurt a Chapel strategy game too badly). Good examples of this are Chancellor/Bureaucrat, or any other card that gains you $2. Even a card like Remodel can supplement a Chapel strategy, and turn that Chapel into a Remodel mid-game, and eventually into Golds/Duchies. The sixth of a time that you get a $5/$2 split, you should probably by a $5-card instead of a Silver. No $5 is worse than a Silver.
Mid-game, when your deck has dwindled, you should almost always play the action card. This is especially true if you are unable to trash 2-3 Coppers/Estates.