It didn't really occur to me to hire a guide in Beijing until I read some recommendations here and booked a woman called Qing to show me around on my first day.
I'm really glad I did this – Qing is a great guide. She and her husband took me to see the Great Wall, but she also did all kinds of practical stuff for me like booking my train tickets to Xining, explaining what all the things in the supermarket are, and she taught me to haggle in the markets. (Er, turns out I am not a good haggler. She got me better prices).
Qing also set me up with a Chinese sim card for my phone and told me to call her from anywhere in China if I had any problems on the rest of my trip. I can't recommend her highly enough! A brilliant way to get acquainted with China at the start of your travels.