Start with making a state Diagram of all inputs and outputs ( including transient switch contact states)
Your inputs are 2 switches Normally Open (NO) connected to ground or Vcc with SIP resistors or discrete R's to the other polarity.
Your Outputs are either 7 segments for Common Cathode LED you specified or using a BCD to 7Seg chip.. Your homework is 7 segment out ( direct non multiplexed)
Next make a truth table for each decimal state 0~9 and define the logic in truth tables then in code for count up and down separate from decoder for binary to 7segment for a decimal number. THis is well documented.
Define overall functions then break down into smaller functions or routines.
Common Cathode means common (-) to ground and positive logic level thru series limited R to turn on LED for 10mA or so. or 200mA Max. to all segments.
The 8th bit can be used for the decimal point or DP LED.
Red LEDs need > 2V. typ (2.5V max) so uC with 3.3 or 5V affects series R per segment choice using Ohm's Law.
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You wont need any transistors for 1 Digit. as the PIC can drive each LED direct with a series R. Keep in mind all drivers have an equivalent series R ( which also has a temperature coefficient) We call this ESR.
Can you see the value of ESR from the slope of these curves? When choosing Vcc and R just subtract the ESR of the driver from the Rs value needed for its Voltage drop required.
Electrical specs like this are always near the end of the 200 pages PIC specs.