I know that dialup connections usually have a bandwidth of 56Kbps and a connection through LAN is like 10 Mbps, 100 Mbps or 1GBit/sec.
How much is it for WIFI connections?
I depends on what kind of a wireless router/access point + wireless card you have on your laptop/phone.
There are different Wi-Fi technologies offering different signaling rates:
Technologies in the same band (b/g/n in 2.4GHz, and a/n in 5GHz) can interconnect as all implementations have always offered backward compatibility.
You should also know that 802.11 has a lot of overhead, so the actual TCP throughput you get under ideal conditions ends up being about 50-60% of the signaling rate.
You can read about the protocol overhead here
Your speed will also be limited by the slower link partner (access point or client station).
For example, if you connect to an 802.11n access point with an 802.11b STA, then the max speed you will get is 11 mbps.