So there are a couple things that might help. Firstly, it never hurts to check the market board. Some of the items you need to turn in for these quests end up getting sold for fairly low prices. If you were struggling with the level 45 weaver quest as an example and could buy the hat you need to turn in for a couple hundred gil that means you only have to focus your crafting talents on the shirt and pants. For most of the quests the game doesnt check if you crafted it yourself(and for the ones that it matters, the items arent tradable). Secondly, you can use high quality materials to get a boost on your crafts. A craft where you use all HQ mats will typically start you with the quality meter half filled for the resulting craft, meaning you only have to do half the work to get it to 100%. Sometimes spending the extra 5 minutes(if you can) to gather high quality cotton(or flax or whatever) before you turn it into threads(and the threads into cloths and then the cloths into finished items) is worth it. And im going to talk about skills but keep in mind that you might just be under-powered to complete the craft in question without luck. If your gear isnt up to date that makes a big difference. Additionally your level matters(both in the crafting formula and in terms of having more/better skills to use), so if all else fails level up a little more then come back and try the quest craft again. Oh, and try to get into the habit of using some sort of crafting food both for the bonus exp and the bonus stats. Even something cheap like stone soup(30 gil on the vendor at the gold saucer and a few other places) can give you a few extra CP that might mean the difference between a success and a fail.

Ok, but lets look at skills. So the basic crafting mini-game is to fill the quality bar as far as you can and fill the progress bar to finish the craft, with the durability meter as your timer. If you open the calculations tab, you can see how much progress each synthesis skill will add and how much quality each touch skill will add. One of the first moves to use is Inner Quiet. Every successful quality move increases its stack(maxes at 11), making quality moves more powerful. High level crafting is mostly about building a high IQ stack, then using a powerful "finishing move" to finish off the quality bar(the level 50 skill you dont have yet is great for this). At your level the strongest finish you could do would be Great Strides(100% boost to next quality move) + Innovation(boosts quality moves for next 4 turns) + Standard Touch(strongest quality move you currently have). The turn sequence for your "finishing move" would look like: Inno, Touch(hasty basic or standard depending on how much CP you have), Touch(same), GS, ST. That would use 30 durability, and 88+ CP. It can help to "finish" the craft before working too much on quality. So you would start with IQ, then use your synth skills(possibly with Veneration - the progress version of Innovation) until you only need 1 more synth to finish, then switch to quality(Final Appraisal can help with this - for up to 5 steps after you activate it any synth that would finish the craft will leave you 1 point short instead therefore guaranteeing you only need 1 more usage to finish). Waste Not(1/2) and Masters Mend give you more durability to work with to finish everything up(either by refilling or by making skills burn half as much), and Tricks of the Trade lets you turn good or excellent material conditions into extra CP to use more moves(otherwise these conditions act as critical hits for your quality moves - avoid using a touch skill on the poor condition if you can because this is more like the opposite of a crit).

I have no idea if that block of rambling will help in any way. When in doubt, try out the option to simulate the craft and try using the skills for practice before committing to burning actual mats in an attempt. Otherwise, continue to ask questions. The more specific, the better the answers will be.