Hi, Forsythia flowers early, on wood that was formed the previous year, so don't prune it yet, or you won't have flowers this year, wait until it finishes flowering, then cut right back into the old wood, {the thicker branches}this will promote the growth of new shoots, which will produce the flowers next year, this can be done annually, so that it keeps on producing new flowering shoots for the following year, Derek.

Derek is right on. Forsythia sets flower bud the previous summer. Once the flowers fade, you'll have a few weeks to prune before it starts setting flower buds for next year. Prune out the old wood, keeping it open and airy.

The "old wood" can mean two different things. If you have some branches that don't produce any leaves and have wood that looks brown rather than green if you scratch a bit of bark off, that's dead wood and you can cut it off at any time.

But what's usually meant is branches that have flowered in the current year, which as Derek said above you should cut off when the flowers have finished. As the bush gets big you will be able to cut further back down the older stems. Just remember never to cut off wood that has grown in the current year.

Its still rather young and should soon start to have more flowers as it matures.

Agree with Stera, the term 'old wood' can be confusing. If your plant is under 10 years old, it doesn't need drastic dead wood removal, all you need to do is, after flowering, cut back all the shoots which have produced flowers, right back as far as you can (this flowered wood is usually what's meant by 'old wood'. Its not that old, only a year...), or at least by half. If that then leaves any long, branches or shoots which haven't flowered that look too long, cut those back by half or two thirds - you won't be doing any more pruning till after it flowers next year, so getting it the right shape after flowering this year is important.

Forsythia naturally has long arching branches and I think it's most beautiful kept to its natural form-instead of tight manicured balls or weird geometric shapes. Simply prune out 1/3 of the old wood - anything that bloomed already. Also any branches that touch the ground will root and start a new plant - something to think about.