For a VFD driving an induction motor, how can I determine the best starting frequency and acceleration time for my motor?

This will be load related. Pump or fan curves will be helpful, torque requirement, time needed to start for system response may require upsizing the drive to meet application.
Too many application questions to be one answer.

Load is a multi-stage centrifugal pump. How can I use curves for that? It's flow rate against Head, efficiency or Brake horse power. As for upsizing, KVA already matches that of the load.

if you are using vfd means normally two type starting mode is there one is coast and another one is automatic or ramp, in pump application you must start ramp mode only because that mode mode only we can achive that smooth starting frequency

The same mechanics old principles are applied: Cd (Demanded torque) = J (Total Intertia moment) x dw (angular speed)/ dt -> w = 2pi/60 rpm. The ramp is can be set in the inverter and it will automatically try to reach nominal speed in certain time if mechanical conditions permit, otherwise it does not go on the ramp set or trips. Everyload has a specific kind of conjugate curve,

Pumps and fans have what we call parabolic torque, however other applications such as cetrifuges have other curves, those must be analyzed and then set on the resources of the drive and power eletronics.

Most of the VFD produced have automatic run check modes to determine load and torque of the motors and pumps. they adjust themselves accordingly.

Inverters usually perform a motor model check and rotor test, and then, we have a speed or torque loop tuning. It may be automatically tuned, but some applications cannot be automatically tuned.

As a side note, if this is a submersible motor with a Kingsburry designed thrust bearing it will nedd to be at 30 HZ, (half speed) in 2 seconds or less. Ramp down is the same, from 30 HZ to 0 in 2 seconds or less. This is to peotect the bearing. Franklin Electric and Hitachi are two examples of this type of motor. Franklin has an online AIM manual, page 40 goes into detail on VFD set ups.

For simple pump and fan applications, generalized thumb rules are applied. It is for critical applications that fine tuning of these are required.

As long as the drive has been appropriately sized for the load requirements, the Acceleration time can be programmed to your specific application needs. Many drives allow you to accelerate and decelerate down to 0.1s, but if the load is too large for the drive, the drive may trip. As far as "starting" frequency goes, it's probably more of a question of minimum allowable frequency while running to maintain proper motor cooling. Other than that, as Shibu stated above, the actual "tuning" is not critical for variable torque pump and fan applications.

It can be also used a monitoring software to display the torque curve so you can adjust the starting time to reduce possible torque overshoot. The shorter time, the larger torque peak can occur and that´s not good for the mechanics.