It is easy, and more convenient than any over complicated statistics program if you ask me. You have two ways you can do this:
(1) The technical way. Just get your data and put it into 3 columns. Put the date, then the SPY daily price, then your stock daily price in columns 1, 2 and 3 respectively. (Use the adjusted close if you get the data from yahoo finance to erase the effect from dividends). Then off to the side a few columns over, make column one the dates, column two the % change for the SPY, and column 3 the % change for the stock you want.
You want to end with daily % changes instead of closing prices. So column 1, 2, and 3 should be the date, then 0.5%, then 1.3% for example. You need it in percentage changes rather than prices.
This erases trending biases.
Next, click the button on excel 2007 on the top left of the screen. Click excel options. Then go to add-ins. Click analysis tool pack and install it. Once that is installed, you can do regressions in excel.
Next, click the data tab, then click data analysis on the right side of the screen. In there, click regression.
Once the screens pop up, you are going to make SPY your X, and your stock Y. You are trying to predict your stock when X happens (the market changes).
Then run the regression. On the printout it will show your variables and betas. In this case you will have one beta for your intercept and one for the market. The one for the market is what people normally refer to "beta." The way I have described this, you will calculate a "daily" beta. Yahoo and most others use a monthly beta calculated over the prior 3 years.
Different betas are used for different goals. For example, a hedge fund may want a beta based on 1-minute intraday data to make high frequency trading ideas. But long term portfolio managers use longer term betas and make longer term investments. Most people would probably find a weekly beta over the prior 1-2 years fits their needs best.
A side note: you can easily change this regression just described into a multifactor model by adding another column, say the price of crude oil. This can greatly improve your accuracy in predicting how your stock behaves because more than just the equity markets are related to stock returns.
The second way you can calculate beta in excel is to just make the data lined up in % returns form, then make a chart of the data and click trend line. Then select chart options and click to show the equation on the chart. It will give you a regression equation with a beta if done correctly.