The Pagan Circle

Does anyone know a simple ritual that I can perform?

Here is something I think you can do on your own without getting into any kind of trouble. You are going to go look for a Druids' Egg.
This is very subjective; a private affair to be taken by ones self alone in the woods near flowing water, lake or pond. You are learning to think not with your mind but to think with your stomach. Your quest requires you to look at stones on the water's edge, in the water, on the bank or not too far from water. If you empty your mind of everyday stuff, meditate, just adjusting to the surrounding space, near water, the hand-sized polished stone will speak to you! Not in normal conversation but somehow, you will just know that is the right stone. Ah, a Druids' Egg!
If done right, you will find a very useful Magickal Tool.
WoundedBear

Winter Solstice Ritual?
Find a place outside where you won't be disturbed and a open fire would be permitted.
Get a magnetic compass, four large rocks, some wine, fruit juice, or even water.
Draw a Circle; actual size is not critical but you want it big enough for ample room. Build a fire in the center. Be reasonable here. Have enough wood handy. This should be right at dusk but before actual Sunset.
Put a stone at each of the Four Cardinal Points using the compass for a good degree of accuracy.
Timing is everything here. Depending on the accuracy of the usual calenders, Farmers' Almanac, the actual time of the Solstice is about the 20-21 of December. With your Circle and Stones, fire, you can witness the Sunset on the 20th then greet the Sunrise on the 21st.
Figure on getting to your Circle about an hour or two before to be certain to have all ready that you will need.
The idea is to stay inside of the Circle. When the fire is out, you may take your leave. Breaking the Circle is not a good idea. Only cats may cross a Magickal Circle with impunity. You have purified the area of the Circle and made it Sacred. This a special place.

The Sky! The Sea! The Earth! That is Sacred to the Druid.

You may of course make up your own words here but keep in mind the Triad. With the Sun going down, you face North, ask the Winds of the North to accept your gift (wine, etc.) by spilling some on the ground. Then turn East to do the same. If you face North, then East would be to your right. Do the same toward South, again another right turn, same thing at West but here you stop. You salute the Sunset, ask for wisdom, finish the wine or whatever beverage you have included as a sacrifice.
This the very broad theory and framework for you to learn to be comfortable with.
Welcoming the Sun, is just that. You are in the darkness just at early twilight. Your Circle with the fire is already burning. If you are really into learning the meaning of all this, nothing would be better than staying up all night, in the Circle, feeding the fire. As the Sun rises up you are facing East. Go ahead and ask for the blessings of the Four Winds of the Cardinal Points and make your sacrifice of the water, juice or wine. This time stopping at East, as just where you started! Salute the Rising Sun and ask for Blessings! Finish the beverage as before.
It is far more important to feel the experience by doing it then worrying if it is "right" as you will learn to trust your own stomach or "gut".
A simpler one might just include a large oak tree or some other majestic tree. Bigger the better. A good sharp knife will be needed. You again will need some kind of sacrifice. Never blood. Never a life. Wine, water, fruit juice, beer when offered with Intent is indeed very potent! You draw a Circle around the tree. Mark off the Four Cardinal Points. Again ask that the Four Winds accept your gift. Start at the North and go to the East then South finishing up at West. For the Sunset you finish at West. For Sunrise you finish up at East.
To draw the Circle, you need a stout stick. So, you find one on a tree. You must ask permission from the tree to cut the branch to fashion the stick. Never just break off a branch! If you really meditate before you do this, you just might hear the tree spirits answer you!
Same as above but once you learn how to communicate with trees, an entire new world opens.
This is just enough to kindle a fire within you. Once you learn from doing just a little, you will know if you have what it takes. Just learning how to vibrate your words is powerful. After you have tried some or all of the above, I can list a few books to seek out.
Let me know what you do and what you experience.
WoundedBear

I don't know a lot about Druid customs, but I'm pretty sure Yule orginated with the Norse. Some see Yule as the New Year, as it is the end of the Holy King's reign, and the beginning of the Oak King's reign. (Shortest night = beginning of longer days = sun's reign over darkness.) In days of old, winter was a very frightening time. The amount of food stored, amount of game available, and the length of the winter all could mean life or death. So, the sun growing in strength was a positive sign for the coming growing season.

I just watched "Christmas Unwrapped: The History of Christmas" by the History Channel. Very interesting! I got it at the library, if you're interested in watching it. The beginning goes into customs before Christianity, including Yule, Saturnalia, Mithraism, etc. Check it out if you get the chance! Actually, there is a ton of information at the library, including the book on Yule by Dorothy Morrison. I love to read about how customs originate!

Whatever you decide to do, enjoy yourself!

Most customs include an all night fire vigil, as WoundedBear suggested. I have yet to stay up all night....it's frickin cold out there! LOL I did join a coven in their fire ritual. They put out every fire in the house (blew out all the pilot lights, turned off the main breaker, etc.--DON'T DO THAT UNLESS YOU KNOW EXACTLY WHAT YOU'RE DOING! GAS LEAKAGE CAN BLOW YOUR HOUSE UP!). Then they used flint and steel to light a flame, and each of us lit our candles from the original candle. Folks went through the house, re-lighting the pilots, turning on the breaker, etc. It was amazing how QUIET a house is without the "fire" running through its veins! You have no idea how much noise electricity makes! Anyway, I used that candle to light all candles I used for magickal workings.

Again, going back to the days of old, the hearth fire was the life of a household. Without the fire, you'd die of hypothermia, couldn't cook food, etc. Folks were very careful in banking their hearth fires at night so they wouldn't go out over night, or burn the house down while they slept. An ancient ritual was to build a bonfire outdoors. Then everyone would dowse their hearth fires, and clear out the old ashes. A new fire was laid, and brought a burning branch from the bonfire to light the fresh hearth fire. Sun/heat/fire...life.

Hope this wasn't too 101 for you. I'm sure you've probably heard it all before. But as long as we're in beginners...there may be someone who doesn't know it yet. And keep in mind, all this may be speculation as most written accounts we have now originated with scribes working for the Church.