To troubleshoot first review all of your wiring ("rat's nest"). Especially check the connections going to the 7-segment displays. Since the schematic doesn't show the pin data for the displays you will need to rely on the spec sheet for the parts you have used. Per my other comment be sure you do have common cathode displays. (Normally there would be low value resistors to limit the current in each abcdefg line, but the CD4026 may limit the current well enough, but if interested about 390 ohms in each line is a safe start.)
Start by reading through the "Working of..." paragraph from the schematic page. Use a voltmeter or logic probe to follow the pulse signal from the top of the push button then to the 555 output. As each pulse gets to the first CD4026 (IC2) you can then check each of the abcdefg pins for changes, each output change from low to high should turn on a new segment.
Unfortunately there is no reset signal included in the schematic. So the only way to clear back to 00 may be to cycle the power. To add a reset you could take the two MR lines and connect them to a single resistor going to gnd (about 5k should work), then connect a switch (push button) that momentarily supplies +5 to the MR-resistor connection.