If

There are two types of 'if' in Welsh - the sort where something is likely to happen and the sort where it's not. 

open
The first type of 'if' is an 'open' condition, and it's pretty simple: If it rains, I have my umbrella. If the cat throws up once more, she's going to the vet. If the car breaks down, we'll have to walk. This kind of 'if' is translated as 'os' for a positive, and 'os na' or 'os nad' for a negative (if... not...).

Os bydd y bws yn hwyr, bydd rhaid inni cerdded. 
Os na fydd 'na ddigon o arian 'da ti, bydda i'n talu.

closed/hypothetical
The second type of 'if' is the sort where whatever it is isn't very likely to occur. If I win the lottery, I'll go on holiday. If the sky falls on my head, I'll get a headache. If only he hadn't sold me into slavery. 

In this case, 'pe' is used along with the conditional of 'bod', ('to be'), and that comes in two main flavours: 

pe baswn i 	pe byddwn i 	if i were
pe baset ti	pe byddet ti	if you were
pe basai fe	pe byddai fe	if he was
pe basai hi	pe byddai hi	if she was
pe basen ni	pe bydden ni	if we were
pe basech chi	pe byddech chi	if you were
pe basen nhw	pe bydden nhw	if they were

You also have these regional variations to deal with as well, some of which drop the 'pe' and all of which have the 'unreality endings' (see also dylwn, gallwn, hoffwn and leiciwn). 

pe bawn i 	pe tawn i	tawn i	pe taswn i	taswn i
pe baet ti	pe taet ti	taet ti	pe taset ti	taset ti
pe bai fe	pe tai fe	tai fe	pe tasai fe	tasai fe
pe bai hi	pe tai hi	tai hi	pe tasai hi	tasai hi
pe baen ni	pe taen ni	taen ni	pe tasen ni	tasen ni
pe baech chi	pe taech chi	taech chi	pe tasech chi	tasech chi
pe baen nhw	pe taen nhw	taen nhw	pe tasen nhw	tasen nhw

Of these, the last column is very common:

Taswn i'n gyfoethog, byddwn i'n mynd i Awstralia.
Bydden nhw'n dod pe byddai rhaid iddyn nhw.

You can also use 'pe' with other unreality verbs, such as gallwn, e.g. Byddwn i'n helpu pe gallwn i.