This will get what you enter in your textbox to your property in the codebehind. Depending on the size of your project I'd consider MVVM to push the code out to the ViewModel, then in the UserControl you'd specify this.DataContext = an instance of your ViewModel.
Xaml:
<UserControl x:Class="SilverlightApplication1.MainPage"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
mc:Ignorable="d"
d:DesignHeight="300" d:DesignWidth="400">
<StackPanel>
<TextBox Text="{Binding Foo,Mode=TwoWay}"/>
<Button Content="Click" Click="Button_Click"/>
</StackPanel>
</UserControl>
Code Behind:
public partial class MainPage : UserControl
{
public string Foo { get; set; }
public MainPage ()
{
InitializeComponent();
this.DataContext = this;
}
}