If the file that you want to read is embedded in the platform project assembly you can use the following code:
var assembly = typeof(MyPage).GetTypeInfo().Assembly;
Stream stream = assembly.GetManifestResourceStream("WorkingWithFiles.PCLTextResource.txt");
string text = "";
using (var reader = new System.IO.StreamReader (stream)) {
text = reader.ReadToEnd ();
}
Make sure that you replace WorkingWithFiles with namespace of your project and PCLTextResource.txt with name of the file.
Check Xamarin documentation at Loading Files Embedded as Resources for more details
If on the other hand you want to create and read/write files at runtime you can use PCLStorage library:
public async Task PCLStorageSample()
{
IFolder rootFolder = FileSystem.Current.LocalStorage;
IFolder folder = await rootFolder.CreateFolderAsync("MySubFolder",
CreationCollisionOption.OpenIfExists);
IFile file = await folder.CreateFileAsync("answer.txt",
CreationCollisionOption.ReplaceExisting);
await file.WriteAllTextAsync("42");
}