My first advice is talk to your neighbours at the allotment. They may have some friendly advice like what does well, and let you know more about what goes on at your site such as whether there is a seed/plant swap or shop, any free deliveries (not all sites have this but worth knowing about), where you can obtain a supply of manure, where the water supply is. Also, it's a nice way to introduce yourself and get to know your neighbours and people generally like to have a chat, especially about the weather and how it is affecting everything, and sometimes a welcome break from working on the plot.
Secondly, all jobs take a lot longer than you planned until you learn to get into a routine. Go with a job list but don't despair if you don't get it all done. Better to spread the work load in little bits over several days a week than try to do it all at once one day a week.
Thirdly, weeds are unforgiving. They germinate and grow at an alarming rate from early spring until midsummer and I've seen many a newbie give up in the first 6 months, but it does get easier if you can keep on top of them. If there are sections of the plot that you won't get cleared in time, it's worth keeping them under some cover, whether you use black plastic, carpet, fabric membrane, cardboard - whatever you are allowed to use on your site and you are comfortable with using until such time you can get round to clearing that area.
Finally, take time to stand back and see what you have achieved and give yourself a pat on the back, rather than dwell on the things that haven't worked. It's a learning experience and not a failure