I assume with constant current you mean, current constant with process, voltage and temperature. There are a few ways to achieve this as,
1) Design a constant voltage source, band-gap or you may want to scale-up the band-gap voltage using an error amplifier and pass device. Then use this voltage to generate constant current, using resistor (external or internal). Mirror this current to get your current source.
Also you may want to go for process trimming to increase the accuracy.
2)Another method would be designing a band-gap circuit, then using the IPTAT, ICTAT and adding them you can get a nearly constant current with temperature. The design can have process trimming.
3) Yet another way could be, generating a VPTAT (again designing a band-gap circuit) and then applying this VPTAT across MOS transistor operating in linear region. Please note, a mos transistor operating in linear region will have resistance across it proportional to temperature. Thus applying VPTAT/R_mos, where R_mos is proportional to temperature, you would get a fairly temperature compensated current source. As usual use current mirrors to mirror the current.