Well, I can never claim that Iam expert in embroidery,but I sure will try to answer your question in the best possible way.Hopefully this will be of some help to you and to all those who want to start doing embroidery.
These are the things you'll need.The bold headings are the items which are unavoidable.You've to have them.
1. Crewel Needles (Embroidery Needles) : There are different types of needles suitable for different types of embroidery. For hand embroidery,you have to use crewel needles. There are many sizes available.Higher the size,finer the needle.Always make sure that the thread just passes through the needle eye and the thread fits in the hole created by the needle in the fabric. Sizes 8 , 9 and 10 would be suitable for a beginner assuming you are embroidering on tightly woven,non-mesh fabric. You can get needle multi-packs if you are unsure of the appropriate needle size for your project. These packs will have a variety of needle sizes to choose from.
Note : If you are opting for a mesh fabric ,then tapestry needles with blunt end would be the choice.
2. Embroidery hoop or rings:
This also comes in different sizes,but I would suggest that you go for a small one and a slightly larger one (not too large) .
3. Fabric :
Cotton or muslin would be the best choice.After a while,you are free to work on the fabric of your choice.
4. Embroidery thread / floss
Anchor and DMC are the primary thread manufacturers.Here again,there are different types of threads,but a beginner should go for cotton threads. You can work with three strands initially and once you get used to it increase or decrease the number of strands.Remember,lesser the strands the more delicate your work will be.
6. Lead pencil / Water soluble marker pen .
7. Dress makers carbon for tracing designs in case you are working on a project.
8. Needle threader (For those who find threading needles difficult)
9. A design to stitch.
You can draw a simple one,or trace, or use iron on transfer patterns.There are plenty of resources in the web .
10. Finally, a reference for the different types of stitches. You can either buy a embroidery book or visit any of the sites mentioned under 'Learning Embroidery ???" on the side panel of this blog.
You can stitch a small and simple pattern or you can just do free hand stitching on your fabric. Vertical lines,horizontal lines,diagonal,zig zag .. anything will do.
What I do is make small samplers of each type of stitch and file it away with a note about it and then try to apply it on a design.
Hope this was helpful.Tell me if you want more info.