A simple example
Here is an example of using Infer.NET to work out the probability of getting both heads when tossing two fair coins.
Variable<bool> firstCoin = Variable.Bernoulli(0.5);
Variable<bool> secondCoin = Variable.Bernoulli(0.5);
Variable<bool> bothHeads = firstCoin & secondCoin;
InferenceEngine engine = new InferenceEngine();
Console.WriteLine("Probability both coins are heads: "+engine.Infer(bothHeads));
The output of this program is:
Probability both coins are heads: Bernoulli(0.25)
which correctly gives the probability of two heads as 0.25 or 1/4.
This short example contains the three key elements of any Infer.NET program:

Definition of a probabilistic model
All Infer.NET programs need a probabilistic model to be defined. This is done in the first three lines above by defining the random variables firstCoin and secondCoin and the specifying the dependent variable bothHeads as a function of these. You can read more about defining models in the Infer.NET modelling API.

Creation of an inference engine
All inference is achieved through the use of an inference engine. This must be created and configured before any inference is performed. The fourth line above creates an inference engine which uses the default inference algorithm (expectation propagation).

Execution of an inference query
Given an inference engine, you can query marginal distributions over variables using Infer(). In the last line of the example, the engine is used to infer the marginal distribution of bothHeads i.e. the probability that both coins turned up heads. The engine returns a Bernouilli distribution which is then printed to the console. You can read more about inference in the section on running inference.
Read on to find out how Infer.NET works.