In 802.11 Wifi, I've read that a wifi adapter (like my laptop's wifi adapter/radio) will use Energy Detection to see if a channel is busy (if a certain energy threshold is detected on the channel, it won't try to use the channel itself). Then there is also Virtual Carrier Sensing, where the wifi adapter will look for Network Allocation Vector timers to see if the channel is free to use.
Do LTE devices like my cellphone use anything like the above?
Yes, LTE has its own set of techniques for dealing with co-channel interference. Collectively, these techniques are known as ICIC (inter-cell interference coordination).
A big difference, though, is that in WiFi (until recently), typically the channel could be either busy or not; there was no concept of sharing the same frequency band, by different allocation of subcarriers to different devices. In LTE, different devices are allocated different "resource blocks" by the base station, so they can be transmitting or receiving in the same band at the same time as other devices using the same base station, and need not be interfering with each other. Read more about OFDMA to understand better how this happens.
For managing/reducing interference between cells, the base stations can coordinate the allocation of resource blocks to different phones.
The allocation of resource blocks is very dynamic, and can change every millisecond, to adapt to channel conditions, data traffic conditions, etc.