There are several easy-to-use products available now. Depending on the size of the desk, you may do well with a spray on poly or lacquer. Also, check the instructions before you buy, the poly's will need to be cleaned and thinned with mineral spirits and the lacquers with...wait for it...lacquer thinner. The spray on stuff may prevent you from needing to purchase the thinners if you are careful about your overspray (do it outside on plastic or hanging from a modified coat hanger in moderate weather).

If you want a nice deep gloss, I suggest buying some cheap brushes that you can throw away and apply it that way. Use some fine sandpaper or some fine steal-wool between each coat to flatten out any bumps or bubbles for a nice smooth finish.

 Good luck, and feel free to ask for clarification if I have confused you.

I just did this exact project! Only I used pine.

I made the amateur mistake of buying "clear" stain from the hardware store -- which is not clear at all for the record. It looked terrible. So I tossed the board and started over.

The second time around, i went with this stuff http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&langId=-1&catalogId=10053&productId=100201939&N=10000003+90276+500953&marketID=276&locStoreNum=2012 and it worked like a charm. It doesn't change the color of the wood at all, but it really draws out the knots and imperfections in the wood. I love it.

I added pictures, but they really exaggerate the change. The top piece is pre-polyurethane and the other pictures are post-polyurethane. These two pieces are actually attached to each other, and the difference doesn't stand out in person. 

It's probably not the nicest solution, but it's insanely cheap, and you can really cake this stuff on and have it look nice. I spill drinks on the desk and they wipe right off... In my humble oppinion, it's the perfect solution for a desktop.

The sealant is up to your preference. You indicated you wanted something thick and clear. Polyurethane is plenty easy to work with, Shiny-ness can be determined by the finish-type: gloss, satin, etc...

I prefer Danish oils, such as those made by Watco (widely available). Their normal oil, non-tinted, does marvels for birch. You might also look at Tung oil, linseed, or teak, or even mineral oil, which is commonly used for items on which food will come in contact.