I think reading the tickets isn´t a problem especially since this enviroment is still new to you. Read it as many times as you want and find necessary.
Of course though i also feel that after sometime things have to (and will) just click and you will be memorizing many orders at a time.
In the beginning of my career i started working as a waiter, then i got a chance to work prep and salads.
Eventually after salads a line cook left and i being very willing got thrown into the line on garnish and hot apps.
I was in the weeds for a week before i started getting a hang of it.
My piece of advice is, "give it your best effort". If you need help ask for it. If you didn´t memorize it look at the order again.
The most important thing is for the customer to get their food, and for you to cook the food maintaining standards.
Communication is also important in the kitchen. Communicate with the brigade and make sure the orders are all getting sent out on time, together. Because its terrible for you to be holding the meal of a table and have food, especially meat and fish dying on the pass.
So communicate, if your not timed with the cooks, ask for help, and be honest. Don´t try to send out something in 5 minutes that you know will take 10.
As time goes by and you gain more experience you will gain the speed. Speed comes with experience and constant practice.
I agree with ice man. I rather take my time and effort to have the food done to perfection, then to send it out and have to refire. Aside from getting the chef p*ssed, you gonna get your brigade pissed, the client is gonna be angry and your just gonna put yourslef in the weeds if you don´t refire quickly.
So yeah take your time, re-read the orders, keep your ears open, ask for help and just cook. Be confident in yourself and don´t give up.