How can I repaint this desk?
If it "chips easily and deep", you need to remove the current finish to get a satisfactory result. 

There are three basic approaches to paint/finish removal

Chemical
There are a number of chemical strippers avaialble. Some are very effective, pretty fast (meaning one application, even if it needs to steep a while) but fairly caustic



Some are less caustic, environmentally friendly and may take a bit longer or be a bit more work


In both cases, apply, let soak, scrape off, wipe clean (and sometimes neutralize) and follow up with sanding as needed.

Scraping
This is pretty useful when the lowest level of finish is not adhering well, or where several layer chip off easily. A heavy duty scraper can be used on thich finishes but can be a bit rough on wood surfaces (potential gouging), and can scrathc metal, so be careful as you get to the base.


There are also cabinet scrapers that are better for thinner finishes and more delicate work. These are also good for curved surfaces and edges.



In Both cases, scraping needs to be followed up by at least a light sanding.

Sanding
This is a brute force approach to finish removal, and generates a lot of dust, some of which could contain lead or other toxic materials. You need to wear a good mask.  This approach is genrall only used when the amount of surface to be cleaned is so large as to make the two other approaches impractical, where the finish is very thin.

Heavy duty sanding uses a belt sander. This approach can rip through paint and wood, and abrade metal. It must be used very cautionsly or you will damage the surface.  But it can be fast. You need to use a succession of grit sizes (moving toward finer as the bulk of finish is removed)



A gentler approach is an orbital sander.  These take off less, are slower, but are more controlable and are much less likely to damage the wood or metal surface. They come in a variety of sizes, and both plug-in and battery models. Again, you will probably need a number of grits as described above. The same cautions apply to the dust.



This type of sander will probably also be needed as the finishing step to follow-up on a removal that uses either chemical stripper or scraper described above.

Repainting
After the finish is removed, you need to clean, prime and paint. It is critical to get all dust off the surface. After vacuuming, a tack rag works very well. A wipe with a rag dipped in mineral spririts is also good to remove any traces. Generally a primer is needed, appropriate to the type of surface. Then finish coats. Enamels give a harder, and often smoother surface. Spray paints give a very smooth finish, but you need to work outdoors. There are a few latex paints that are pretty tough once dry. In any case, several coats are generally needed to give both full coverage and a slightly thicker coat for better wear.