My suggestions are --
1 Go though the clues and try to solve as many as you can.
2 There is only one clue for each letter. However, there are two places in the grid where answers must start with the same letter. They are in the NE and SE corners and the answers are 8,7 and 4,5 (or 7,8 / 5,4). Look for clues which fit that pattern.
3 Of the three 15-letter answers, two fit the 7,8 pattern. The clue for what would be 5a and 5d in a conventionally numbered crossword must therefore begin with either L or M. That was enough for me to solve the M clue and write it in. That answer will give you the starting letters for 6d, 7d and 8d. It will also give you the start of the 8 letter-answer about halfway down. That answer will in turn give you first letter of the the 9-letter answer running downwards, and that answer will give you the first letter of the two 6-letter answers running across, one of which is on the bottom line .
4 It is unnecessary to write in the notional numbers. I am doing this only to assist in providing this explanation. I haven't numbered thtough to the end as it is quite easy to miscount and confuse everyone.
5 One answer begins with Q which must usually be followed by U. Now that you have eliminated 5a (which must begin with L or M), there are only three places where the 8-letter word beginning with Q can go. One of these (in the bottom left corner) would mean that U was the last letter of 2d. That is possible, but unlikely. It means that either; (1) the answer to 2d does not end with U so that the Q word cannot go in the bottom, left-hand corner; or (2) the answer to 2d is unusual and probably a foreign word which ends in U.
6 There are only two 4,5 answers. If you solve them you will see that one has words beginning with different letters, so that this answer cannot be the clue that fits into the 4,5 in the SE corner.
7 I would not have said this had it not been mentioned already, but the answer that you have been given by scorpiojo resolves the L/M question, and also gives you two more starting letters. Giving you the answer in that way does not really explain how the puzzle works but it may help to get you started. For example, it means that you are looking for a five letter word beginning with Z for 3d.
8 One answer is a four-letter word beginning with X. There is only one place where that answer can go.
9 It is best to start with answers of which you are quite sure. Alphabetical puzzles like this are a pleasant change. There was general agreement (which I share) on the Guardian site that this was an entertaining but not especially difficult example of its type, so a good one to start on.
Good luck!