Just pass in the current Context to the Adapter constructor and store it as a field. Then inside the onClick you can use that context to call startActivity().
pseudo-code
public class MyAdapter extends Adapter {
private Context context;
public MyAdapter(Context context) {
this.context = context;
}
public View getView(...){
View v;
v.setOnClickListener(new OnClickListener() {
void onClick() {
context.startActivity(...);
}
});
}
}