1. Loading the model

To load a model file into the actual game, you can use the utility methods in the BbModelLoader and AjModelLoader classes.
Models required in mods should be retrieved by ID, but it's also possible to load files from the server.
Note that these models are not cached by BIL. They are safe to reuse and should be cached when possible

public static final Model MODEL_FROM_ID = BbModelLoader.load(new ResourceLocation("namespace", "path"));
public static final Model MODEL_FROM_FILEPATH = BbModelLoader.load("file/path/example.bbmodel");

These Model objects can be used with BIL's custom implementations of Polymer's ElementHolder.
Anything extending AbstractAnimatedHolder supports it.

2. Entity Attachments

BIL models can be attached to entities.
Writing a custom entity with model works mostly the same as writing one normally.
You just have to implement AnimatedEntity and initialize an EntityHolder in the constructor with the model.

public class RedstoneGolem extends Monster implements AnimatedEntity {
    public static final ResourceLocation ID = new ResourceLocation("bil", "redstone_golem");
    public static final Model MODEL = BbModelImporter.load(ID);
    private final EntityHolder<RedstoneGolem> holder;

    public RedstoneGolem(EntityType<? extends Monster> type, Level level) {
        super(type, level);

        // Creates model holder with out of the box support for most LivingEntity features.
        // Note that it is always possible to write your own or override some of their methods.
        this.holder = new LivingEntityHolder<>(this, MODEL);

        // Attaches the holder to this entity in Polymer.
        // Make sure that ticking is enabled, as it is required for model updates.
        EntityAttachment.ofTicking(this.holder, this);
    }

    @Override
    public EntityHolder<RedstoneGolem> getHolder() {
        return this.holder;
    }
}

3. Other Attachments

While BIL is mostly targeted towards entities, it is possible to attach model holders to other things.
Polymer provides a few of its own other attachments, like ChunkAttachment and BlockBoundAttachment.
You can attach your model holder those aswell.

4. Variants and Animations

One thing BIL can't automatically do for you is decide when certain animations or variants should be used.
To do this, every holder provides an Animator and VariantController, which can for example be used like this:

Animator animator = holder.getAnimator();

// Completely stops the animation named 'idle'.
animator.stopAnimation("idle");

// Pauses the animation named 'walk'.
animator.pauseAnimation("walk");

// Plays the melee animation with priority 10.
animator.playAnimation("melee", 10); 

VariantController controller = holder.getVariantController();

// Sets the variant to the variant named 'hurt' if the current variant is default.
if (controller.isDefaultVariant()) {
    controller.setVariant("hurt");
}