From the SRK wiki...
"Mai only has a few combos, let's check 'em out.
cr.C/cl.C xx Ryuu Enbu (qcb+P)
cr.C xx Ryuu Enbu (qcb+P)/Killing Ninja Strike (hcf+K)/Super Killing Ninja Strike (qcb,hcf+K)
cr.B,cl.A xx C Ryuu Enbu (qcb+C)/B Killing Ninja Strike (hcf+B)/Super Killing Ninja Strike (qcb,hcf+K)
f+B, cr.C xx Ryuu Enbu (qcb+P)/Killing Ninja Strike (hcf+K)/Super Killing Ninja Strike (qcb,hcf+K)
corner only, meaty A Ryuu Enbu (qcb+A), st.A/B
corner only, meaty A Ryuu Enbu (qcb+A), cr.C xx Ryuu Enbu (qcb+P)/Killing Ninja Strike (hcf+K)/Super Killing Ninja Strike (qcb,hcf+K)
corner only, meaty A Ryuu Enbu (qcb+A), B Killing Ninja Strike (hcf+B)/Super Killing Ninja Strike (qcb,hcf+K)
Note that cr.C is hit-confirmable, so never do hcf+K or qcb,hcf+K on block obviously. For the cr.B combo, input cr.B, qcb+A, hcf+K for the super input."
"Takuma has a few different variations that lead into super, so experiment and find the one you're most comfortable with.
cr.A/Bx2,f+A xx C Fireball (qcf+C)
cr.A/Bx3,f+A (optional) xx A Ryuuko Ranbu (qcf,hcb+A)
cr.A/Bx2,f+b (optional) xx A Ryuuko Ranbu (qcf,hcb+A)
cr.C xx D Flying Kick (charge d/b,f+D), Rapid Punches (f,b,f+P)/st.CD xx A Fireball (qcf+A), B Running Kneebash Grab (hcb+B) (unblockable fireball setup if they roll)
Always use cr.B to start, then switch to cr.A if you want for the last light hit, but you can also just use cr.B for all the hits. Remember to use the hold buffering method if you use f+A (ie hold down B and use qcf+A for f+A input, then hcb+A to super). That way you won't get a fireball. Using f+B won't require this, but it has less range. Personally I just use cr.Bx3 xx super."
That should be a good start for you with Takuma. He can be a beast in KOF '98 and quite a fun character to use.