Like its neighbours in Central Europe, the Czech Republic has two quite distinct seasons between a fairly cold winter with abundant snow fall and summers which are often stiflingly hot. Think about that when you're packing your bags for the country. The ideal is to go there between seasons, in May, when the apple and pear trees on Letna Hill in Prague are in flower, or in September, when the temperatures remain pleasant and the numerous tourists have left.
If you're thinking about coming in winter arm yourself with warm clothes, especially if you're coming to Prague where long walks (even if interspersed with stops in the Czech inns) can end up being freezing. In summer, light clothes suffice for the capital Prague and the big cities in the Czech Republic even though a raincoat is always recommended. Moreover think about a suitable outfit if you're planning to go out, whether it's to a restaurant, the theatre, or the opera. It's always a must culturally to dress well for this type of outing.
If you're planning to spend a little time in the Czech countryside or in the country's national parks, good shoes can be a very good idea. Actually, the Czech mountains, despite their fairly limited altitude, have several hiking paths.