[Browsable(true)]
public int MyProperty
{
    get
    {
        // Insert code here.
        return 0;
    }
    set
    {
        // Insert code here.
    }
}

// Gets the attributes for the property.
AttributeCollection attributes =
   TypeDescriptor.GetProperties(this)["MyProperty"].Attributes;

// Checks to see if the value of the BrowsableAttribute is Yes.
if (attributes[typeof(BrowsableAttribute)].Equals(BrowsableAttribute.Yes))
{
    // Insert code here.
}

// This is another way to see whether the property is browsable.
BrowsableAttribute myAttribute =
   (BrowsableAttribute)attributes[typeof(BrowsableAttribute)];
if (myAttribute.Browsable)
{
    // Insert code here.
}

AttributeCollection attributes =
    TypeDescriptor.GetAttributes(MyProperty);
if (attributes[typeof(BrowsableAttribute)].Equals(BrowsableAttribute.Yes))
{
    // Insert code here.
}