The way May approached negotiations with the EU was from a position of weakness and was doomed to fail. I wonder how much of her approach was a result of political constraints or how much of it was a result of incompetence or deliberate sabotage by her or the bureaucracy.
1) She should have made deals or conditional deals with other trading partners before submitting Article 50. This way she would have had a good BATNA option in the case negotiation with the EU failed. The EU may have been more reasonable if they realised the UK had less to lose from a failed negotiation. Of course there were problems with this approach. Firstly, it might not have been politically possible for her to delay submitting Article 50. Secondly, if you are in the EU you are not meant to negotiate trade deals with other countries. However, there is no reason for the EU to find out and I guess more importantly the EU has no real way to credibly punish the UK for that action if the UK alternative was just to submit Article 50 straight away.
2) She should have tried to get assurances from other countries in the Council to negotiate good trading terms before submitting Article 50. Yes. This is not how the EU works and the Commission is probably more likely to act in a way that hurts EU citizens but benefits the EU as an institution and unfortunately they are the ones in control of the text of such agreements. But if there was strong pressure from the Council then the Commission would look bad if they scuttled a free trade deal that looked to benefit all parties.
Free trade is meant to be good for both parties [There seems to be strong consensus from economists on this point!]. So assuming both parties are acting in good faith with their citizens welfare as a priority then surely the outcome of negotiations should be a good trade deal.