gistfile1.js

var cell = new Array(3);
for (i = 0; i < 3; i++) {
    cell[i] = new Array(3);

}
var newCell = new Array(3);
for (i = 0; i < 3; i++) {
    newCell[i] = new Array(3);
}

// you do the same thing twice above; it would be worth extracting that to a function

var i = 0, j = 0;  // these are re-defined in the for loops anyway, so this line is redundant

function checkArray(cell) {
    console.log("check center call");
    for (var i = 0; i <= 2; i++) {
        console.log("check center i= ", i);

        for (var j = 0; j <= 2; j++) {
            console.log("check center j= ", j);

            if (cell[i][j] === 1) {
                cell[i][j] = 1;
                console.log("check entering one");
            } else {
                cell[i][j] = 0;
                console.log("check entering zeros");

            }
        }
    }
    console.log("check end call", cell);
    return cell;
}
function neighbour(returnCell) {
    var totalCells = 0; var cell2 = returnCell;  // this *won't* create a copy of the cell!
    console.log("check center call second function");

    // why f and k here rather than i and j?
    for (var f = 1; f < 2; f++) { //iterate through rows
        console.log("check center second function f= ", f);
        for (var k = 1; k < 2; k++) { //iterate through columns
            console.log("check center second function j= ", k);

            //add up the total values for the surrounding cells

            totalCells += cell2[f - 1][k - 1]; //top left
            totalCells += cell2[f - 1][k]; //top center
            totalCells += cell2[f - 1][k + 1]; //top right

            totalCells += cell2[f][k - 1]; //middle left
            //totalCells += cell2[f][k]; //middle center 
            totalCells += cell2[f][k + 1]; //middle right

            totalCells += cell2[f + 1][k - 1]; //bottom left
            totalCells += cell2[f + 1][k]; //bottom center
            totalCells += cell2[f + 1][k + 1]; //bottom right

            console.log("check totalCells second function totalCells= ", totalCells);

            //apply the rules to each cell
            if (cell2[f][k] === 0) {
                console.log("check if second function totalCells= ", totalCells);
                switch (totalCells) {
                    case 3:
                        newCell[f][k] = 1; //if cell is dead and has 3 neighbours, switch it on
                        break;
                    default:
                        newCell[f][k] = 0; //otherwise leave it dead
                }
            // no need for else if - if it's not 0 it must be 1
            } else if (cell2[f][k] === 1) { //apply rules to living cell
                console.log("check if second function totalCells= ", totalCells);
                switch (totalCells) {
                    case 0:
                    case 1:
                        newCell[f][k] = 0; //die of lonelines
                        console.log("check case 1 = ", totalCells);
                        console.log("die of lonelines ");
                        break;
                    case 2: console.log("die of lonelines "); break;
                    case 3:
                        newCell[f][k] = 1; //carry on living
                        console.log("carry on living ");
                        break;
                    case 4: console.log("carry on living "); break;
                    case 5: console.log("carry on living "); break;
                    case 6: console.log("carry on living "); break;
                    case 7: console.log("carry on living "); break;
                    case 8:
                        newCell[f][k] = 0; //die of overcrowding
                        console.log("die of lonelines ");
                        break;
                    default:
                        newCell[f][k] = 0; //

                }

            }
        }


        for (var f = 0; f <= 2; f++) { //iterate through rows
            // console.log("check lastcall For = ");

            for (var k = 0; k <= 2; k++) { //iterate through columns
                newCell[f][k] = cell2[f][k];
            }
        }
    }
    return newCell;  // if you return the new cell, you should create it inside this function
}
var array = [[0, 0, 0], [0, 1, 1], [0, 0, 0]];
var retChec = checkArray(array);
console.log("retChec = ", retChec);

console.log("checking the arrary = ", retChec);  // this is the same thing you just logged, is that right?
console.log("checking the neighbours of cells ", neighbour(retChec));