If you know the size of the array before you start reading the file, you can preallocate the array before you start reading the file. Otherwise you can read data into an ArrayList of ArrayLists and then convert those into a 2-D array once you know the number of rows & columns. In either case you can use a FileReader and String.split() to parse each line. Something like this (ignoring exception handling and potential subtleties with string quoting and character escapes):
String[][] strings = new String[10][5]; // If you know the size of the arrays before reading the file
ArrayList<ArrayList<String>> strings = new ArrayList<ArrayList<String>>(); // If you don't know sizes
// Read the file
BufferedReader br = new BufferedReader(new FileReader("file.csv"));
String line;
while (line = br.readLine() != null) {
String[] values = line.split(",");
// Copy the values from the values array into the array of strings or the list of lists
}
}