Short answer

For those who are already familiar with setting up a RecyclerView to make a list, the good news is that making a grid is largely the same. You just use a GridLayoutManager instead of a LinearLayoutManager when you set the RecyclerView up.

recyclerView.setLayoutManager(new GridLayoutManager(this, numberOfColumns));

If you need more help than that, then check out the following example.

Full example

The following is a minimal example that will look like the image below.

Start with an empty activity. You will perform the following tasks to add the RecyclerView grid. All you need to do is copy and paste the code in each section. Later you can customize it to fit your needs.

Add dependencies to gradle
Add the xml layout files for the activity and for the grid cell
Make the RecyclerView adapter
Initialize the RecyclerView in your activity

Update Gradle dependencies

Make sure the following dependencies are in your app gradle.build file:

compile 'com.android.support:appcompat-v7:27.1.1'
compile 'com.android.support:recyclerview-v7:27.1.1'

You can update the version numbers to whatever is the most current.

Create activity layout

Add the RecyclerView to your xml layout.

activity_main.xml

<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <android.support.v7.widget.RecyclerView
        android:id="@+id/rvNumbers"
        android:layout_width="match_parent"
        android:layout_height="match_parent"/>

</RelativeLayout>

Create grid cell layout

Each cell in our RecyclerView grid is only going to have a single TextView. Create a new layout resource file.

recyclerview_item.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="horizontal"
    android:padding="5dp"
    android:layout_width="50dp"
    android:layout_height="50dp">

        <TextView
            android:id="@+id/info_text"
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:gravity="center"
            android:background="@color/colorAccent"/>

</LinearLayout>

Create the adapter

The RecyclerView needs an adapter to populate the views in each cell with your data. Create a new java file.

MyRecyclerViewAdapter.java

public class MyRecyclerViewAdapter extends RecyclerView.Adapter<MyRecyclerViewAdapter.ViewHolder> {

    private String[] mData;
    private LayoutInflater mInflater;
    private ItemClickListener mClickListener;

    // data is passed into the constructor
    MyRecyclerViewAdapter(Context context, String[] data) {
        this.mInflater = LayoutInflater.from(context);
        this.mData = data;
    }

    // inflates the cell layout from xml when needed
    @Override
    @NonNull 
    public ViewHolder onCreateViewHolder(@NonNull ViewGroup parent, int viewType) {
        View view = mInflater.inflate(R.layout.recyclerview_item, parent, false);
        return new ViewHolder(view);
    }

    // binds the data to the TextView in each cell
    @Override
    public void onBindViewHolder(@NonNull ViewHolder holder, int position) {
        holder.myTextView.setText(mData[position]);
    }

    // total number of cells
    @Override
    public int getItemCount() {
        return mData.length;
    }


    // stores and recycles views as they are scrolled off screen
    public class ViewHolder extends RecyclerView.ViewHolder implements View.OnClickListener {
        TextView myTextView;

        ViewHolder(View itemView) {
            super(itemView);
            myTextView = itemView.findViewById(R.id.info_text);
            itemView.setOnClickListener(this);
        }

        @Override
        public void onClick(View view) {
            if (mClickListener != null) mClickListener.onItemClick(view, getAdapterPosition());
        }
    }

    // convenience method for getting data at click position
    String getItem(int id) {
        return mData[id];
    }

    // allows clicks events to be caught
    void setClickListener(ItemClickListener itemClickListener) {
        this.mClickListener = itemClickListener;
    }

    // parent activity will implement this method to respond to click events
    public interface ItemClickListener {
        void onItemClick(View view, int position);
    }
}

Notes

Although not strictly necessary, I included the functionality for listening for click events on the cells. This was available in the old GridView and is a common need. You can remove this code if you don't need it.

Initialize RecyclerView in Activity

Add the following code to your main activity.

MainActivity.java

public class MainActivity extends AppCompatActivity implements MyRecyclerViewAdapter.ItemClickListener {

    MyRecyclerViewAdapter adapter;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        // data to populate the RecyclerView with
        String[] data = {"1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48"};

        // set up the RecyclerView
        RecyclerView recyclerView = findViewById(R.id.rvNumbers);
        int numberOfColumns = 6;
        recyclerView.setLayoutManager(new GridLayoutManager(this, numberOfColumns));
        adapter = new MyRecyclerViewAdapter(this, data);
        adapter.setClickListener(this);
        recyclerView.setAdapter(adapter);
    }

    @Override
    public void onItemClick(View view, int position) {
        Log.i("TAG", "You clicked number " + adapter.getItem(position) + ", which is at cell position " + position);
    }
}

Notes

Notice that the activity implements the ItemClickListener that we defined in our adapter. This allows us to handle cell click events in onItemClick.

Finished

That's it. You should be able to run your project now and get something similar to the image at the top.

Going on

Rounded corners

Use a CardView

Auto-fitting columns

GridLayoutManager - how to auto fit columns?

Simple Android grid example using RecyclerView with GridLayoutManager (like the old GridView)