Uhm well, I know a little trick to learn all the -TE form conversions, you have to know the MASU form though =P.
Ending sylabe of the verb in masu form -------
changes to:
- I, CHI, RI --------- -TTE
Example: ARAI~MASU (ends with I) ---- ARATTE
TACHI~MASU (ends with CHI) --- TATTE
- NI, MI, BI --------- - NDE
Example: NOMI~MASU (ends with MI) ---- NONDE
SHINI~MASU (ends with NI) ----- SHINDE
- KI ---- -ITE
Example: KAKI~MASU (ends with KI) -- KAITE
- GI ---- -IDE
Example: OYOGI~MASU (ends with GI) -- OYONDE
- SHI ---- -SHITE
Example: BENKYOUSHI~MASU -- BENKYOUSHITE
And the verbs Shimasu and Kimasu are SHITE and KITE respectively...
I hope this little explanation isn't confusing =P, I'm not really good explaining things hehe