Like learning any new skill lacemaking takes time, perseverance and an initial outlay for equipment. The good thing is that apart from a few consumables, like thread, the equipment you buy will last you many years - my original straw pillow is now 35 years old and still serviceable.
Many items can be bought second hand on sites such as ebay or gumtree. Harlequin Lace and Mainly Lace both sell starter kits.
In each section below I have given the names of some suppliers as a starting point for you to investigate equipment - there are many more and you should enjoy searching the internet before you plump.
There are two types of pillow, the first type being flat, and either round or square. More expensive models have blocks or rollers to facilitate moving the lace up if you are making a large edging, but a simple pillow is adequate for many items and there are techniques for moving lace without the need for a block pillow. I would advise you to purchase one of at least 18 inches (approx. 45 cm) in diameter, smaller ones can feel cramped when you start to use more bobbins.
The second type of pillow is the Honiton pillow, this resembles a squashed football and is filled with straw. I am not aware of any suppliers for new pillows of this type. Honiton lace is very fine, and unless your eyesight is exceptional, I do not recommend a beginner to start with this, especially when only attending a short course.
Pillow suppliers include:
Harlequin Lace - Polystyrene
Mainly Lace - Polystyrene and the traditional (more expensive) straw filled ones.
Again there are two types - the Midland bobbin which has spangles (beads) on the bottom and the Honiton bobbin, which is much more slender and has a pointed end with no spangle.
Lacemaking uses bobbins in pairs, so that is how we count them. You will need an absolute minimum of 12 pairs (24 bobbins), but 20 pairs will give you enough to move onto other patterns.
Bobbin suppliers include:
Traditionally brass, but realistically for the first couple of pieces dressmaking pins will serve.
As you become more adept at making lace you will need to buy reels of thread that are manufactured for the purpose. Initially Perle 8 will be suitable to practice the stitches and complete a simple pattern. A reel of ordinary machine twist would be useful to have with you in case you need something finer. Please bring along a pair of sharp scissors suitable for cutting thread.
Two large pieces of plain, soft, lint free hemmed cotton fabric (approx18" square). One will be used over the pattern and under the bobbins to stop the threads rubbing and the other will be used to cover your pillow when you are not working.
All other equipment can be loaned if needed.