Determine if the device is a smartphone or tablet?

1. First and Best Approach:

Way to set a boolean value in a specific value file (as res/values-sw600dp/):

<resources>
    <bool name="isTablet">true</bool>
</resources>

Because the sw600dp qualifier is only valid for platforms above android 3.2. If you want to make sure this technique works on all platforms (before 3.2), create the same file in res/values-xlarge folder:

<resources>
    <bool name="isTablet">true</bool>
</resources>

Then, in the "standard" value file (as res/values/), you set the boolean to false:

<resources>
    <bool name="isTablet">false</bool>
</resources>

Then in you activity, you can get this value and check if you are running in a tablet size device:

boolean tabletSize = getResources().getBoolean(R.bool.isTablet);
if (tabletSize) {
    // do something
} else {
    // do something else

2. Second Approach:

DisplayMetrics metrics = new DisplayMetrics();
getWindowManager().getDefaultDisplay().getMetrics(metrics);
int width = metrics.widthPixels;
int height = metrics.heightPixels;

if (SharedCode.width > 1023 || SharedCode.height > 1023){
   //code for big screen (like tablet)
}else{
   //code for small screen (like smartphone)
}

3. Third Approach:

My assumption is that when you define 'Mobile/Phone' you wish to know whether you can make a phone call on the device which cannot be done on something that would be defined as a 'Tablet'. The way to verify this is below. If you wish to know something based on sensors, screen size, etc then this is really a different question.
Also, while using screen resolution, or the resource managements large vs xlarge, may have been a valid approach in the past new 'Mobile' devices are now coming with such large screens and high resolutions that they are blurring this line while if you really wish to know phone call vs no phone call capability the below is 'best'.

TelephonyManager manager = (TelephonyManager)context.getSystemService(Context.TELEPHONY_SERVICE);
        if(manager.getPhoneType() == TelephonyManager.PHONE_TYPE_NONE){
            return "Tablet";
        }else{
            return "Mobile";
        }