to iterate over the values use loops:

 int[][] matrix   
 //...
 for(int row[] : matrix)
     for(int cell : row){
      //do something with cell
    }

to access the coordinates based on the value you would need some sort of double hashmap (look a at java.util.HashMap) but i am aware of nothing that does so directly

Unless your grid is sorted in some way then you probably won't do any better than a brute force search.

For iterating, I think it would be something like this (syntax might be off a bit, I haven't dealt with arrays in java for a while.):

int[][] grid;  // just assuming this is already assigned somewhere

for(int x = 0 ; x < grid.length ; x++) {
  int[] row = grid[x];
  for(int y = 0 ; y < row.length ; y++) {
    int value = row[y];
    // Here you have the value for grid[x][y] and can do what you need to with it
  }
}

For searching you'd probably need to use that to iterate, then return once you've found it.

If you might be looking up the position of the same value multiple times then you might want to memoize the results using a hashtable.

To iterate over all the elements in the grid try this:

int grid[][] = new int[10][10];

for(int i = 0; i < grid.length(); ++i) {
    for(int j = 0; j < grid[i].length(); ++j) {
        // Do whatever with grid[i][j] here
    }
}

Use nested for loops to iterate over the x and y dimensions, which lets you go over each value, one at a time.

For inputting a value, just do the same as above, but look for a match to your requested value.

You'll be happiest if you block all these collections inside a single class and don't expose them in any way.

This means moving your search and lookup routines into this class as well.

For storage, everybody's covered iterating, add a hashtable and a lookup. I put this comment on nickolai's post:

Store new Integer(ix + iy * 1000) as the value in your hash table. If your y index can go over 1000 use a bigger number--ints are really big. To get it back use ix=val%1000, iy=val/1000.

If your array and hashtable are encapsulated in the same class, the rest of your code will be pretty easy to write and a lot cleaner.

There's generally no way to find the specific coordinates of a particular value except by going through the array and searching for it. However, if the values in the array are guaranteed to be unique (i.e. each value only occurs in one cell), you could maintain a separate array as an index, which stores the coordinates of each value indexed by the value.